DOANE - STAT - Chap 006

Chapter 06Discrete Probability Distributions True / False Questions 1. A random variable is a function or rule that assigns a numerical value to each outcome in the sample space of a stochastic (chance) experiment. True False 2. A discrete random variable has a countable number of distinct values. True False 3. The expected value of a discrete random variable E(X) is the sum of all X values weighted by their respective probabilities. True False 4. A discrete distribution can be described by its probability density function (PDF) or by its cumulative distribution function (CDF). True False 5. A random variable may be discrete or continuous, but not both. True False 6. To describe the number of blemishes per sheet of white bond paper, we would use a discrete uniform distribution. True False 7. The outcomes for the sum of two dice can be described as a discrete uniform distribution. True False 8. A discrete binomial distribution is skewed right when π > .50. True False 9. When π = .70 the discrete binomial distribution is negatively skewed. True False 10 The Poisson distribution describes the number of occurrences within a . randomly chosen unit of time or space. True False 11 The Poisson distribution can be skewed either left or right, depending . on λ. True False 12 Although the shape of the Poisson distribution is positively skewed, it . becomes more nearly symmetric as its mean becomes larger. True False 13 As a rule of thumb, the Poisson distribution can be used to approximate . a binomial distribution when n ≥ 20 and π ≤ .05. True False 14 The hypergeometric distribution is skewed right. . True False 15 The hypergeometric distribution assumes that the probability of a . success remains the same from one trial to the next. True False 16 The hypergeometric distribution is not applicable if sampling is done . with replacement. True False 17 As a rule of thumb, the binomial distribution can be used to . approximate the hypergeometric distribution whenever the population is at least 20 times as large as the sample. True False 18 An example of a geometric random variable is the number of pine . trees with pine beetle infestation in a random sample of 15 pine trees in Colorado. True False 19 Calculating the probability of getting three aces in a hand of five cards . dealt from a deck of 52 cards would require the use of a hypergeometric distribution. True False 20 The Poisson distribution is appropriate to describe the number of . babies born in a small hospital on a given day. True False 21 The gender of a randomly chosen unborn child is a Bernoulli event. . True False 22 The Poisson distribution has only one parameter. . True False 23 The standard deviation of a Poisson random variable is the square root . of its mean. True False 24 Customer arrivals per unit of time would tend to follow a binomial . distribution. True False likely. is a: A. is independent of the parameters of the distribution. is best avoided if at all possible. C. B. B. D. True False Multiple Choice Questions 27 A discrete probability distribution: . 28 The number of male babies in a sample of 10 randomly chosen babies . 29 A discrete random variable: . D. binary random variable. . can be treated as continuous when it has a large range of values. B. C. D. can assume values between -1 and +1. A. assigns a probability to each possible value of the random variable. continuous random variable. failure) in the Bernoulli model are equally . is a listing of all possible values of the random variable. C. A. is usually uniformly distributed. Poisson random variable.25 The two outcomes (success. cannot be treated as continuous. True False 26 The expected value of a random variable is its mean. . binomial random variable. The hypergeometric distribution is symmetric. B. Assuming the probability of success (making a free throw) is constant from trial to trial. C. the first free throw in basketball. The number of correct answers on a statistics exam 31 Which is a not a discrete random variable? . what type of distribution does X follow? A. The number of defects in a 4 × 8 sheet of plywood B. B. A. The time until failure of a vehicle headlamp D. D. The binomial distribution may be skewed left or right. C.30 Which is not a discrete random variable? . Binomial Poisson Hypergeometric Geometric . A. 33 The random variable X is the number of shots it takes before you make . The discrete uniform distribution is always symmetric. The number of births in a hospital on a given day The number of fives obtained in four rolls of a die The hourly earnings of a call center employee in Boston The number of applicants applying for a civil service job 32 Which statement is incorrect? . D. A. C. B. The Poisson distribution is always skewed right. The number of female passengers who board a plane C. D. which probability model would you use to . Binomial Poisson Hypergeometric Geometric 36 Which model would you use to describe the probability that a call. D. D. assuming a constant probability of a burned-out tube? A. Binomial Poisson Hypergeometric Geometric 35 Which distribution is most nearly appropriate to describe the number of . Binomial Poisson Hypergeometric Geometric . describe the number of accidents at the intersection of two streets? A. fatalities in Texas in a given year due to poisonous snakebites? A. C. number of burned-out fluorescent tubes in a classroom with 12 fluorescent tubes. D. center operator will make the first sale on the third call. B. D. assuming a constant probability of making a sale? A.34 Which probability model is most nearly appropriate to describe the . Binomial Poisson Hypergeometric Geometric 37 In a randomly chosen week. C. B. C. B. B. C. m. A. D. Binomial Poisson Hypergeometric Geometric . C. B. Binomial Poisson Hypergeometric Geometric 41 Which model best describes the number of blemishes per sheet of . C.38 Which model best describes the number of nonworking web URLs . B. B. ("This page cannot be displayed") you encounter in a randomly chosen minute while surfing websites for Florida vacation rental condos? A. C. D. D. Poisson Hypergeometric Binomial Uniform 40 Which model best describes the number of incorrect fare quotations by . white bond paper? A. a well-trained airline ticket agent between 2 p. C. D. on a particular Thursday. Binomial Poisson Hypergeometric Geometric 39 Which probability model would you use to describe the number of . B.m. and 3 p. damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers? A. Binomial Poisson Hypergeometric Geometric 43 The number of people injured in rafting expeditions on the Colorado . drawing for a free mule ride. monitored at random. of which 4 are incorrect. Binomial Poisson Hypergeometric Geometric . B.42 To ensure quality. Binomial Poisson Hypergeometric Geometric 44 On a particular Thursday in August. Ten of the entrants are European tourists. B. C. which model best describes the number of incorrect quotations Bob will make? A. ticket agent Bob gives 40 fare quotations. B. D. Which model best describes the number of European tourists in the random sample? A. D. D. Five entrants are selected at random to get the free mule ride. customer calls for airline fare quotations are . C. 40 Grand Canyon tourists enter a . C. On a particular Thursday afternoon. River on a randomly chosen Thursday in August is best described by which model? A. In a random sample of 8 of these customer calls. D. first twins are delivered? A. s = 50 .45 Which model best describes the number of births in a hospital until the . Binomial Poisson Hypergeometric Geometric 46 On a randomly chosen Wednesday. which probability model would you . customers served at a certain California Pizza Kitchen until the first customer orders split pea soup? A. n = 10. C. C. π = . Poisson with λ = 25. B. A. B. D. B. Binomial Poisson Hypergeometric Geometric 47 Which probability model would you use to describe the number of .05 Hypergeometric with N = 100. Binomial Geometric Uniform Poisson 48 Which distribution has a mean of 5? . D. C. B. C. use to describe the number of convenience store robberies in Los Angeles? A. Binomial with n = 200. 50 A charity raffle prize is $1. If it comes up 1 or 2 you win $2. Find the expected winnings. At what ticket price would a ticket buyer expect to break even? A. B. One winner will be selected at random. If it comes up 3.00 51 A die is rolled. D. If it rolls to a 4. $0.25 $0.00 52 A fair die is rolled. D. C. C. heads in 200 flips of a fair coin. B. D. defective CDs in a spool containing 15 CDs. 2. C.50 $3. C. . face cards in a bridge hand of 13 cards. or 3 you win $2. the one that most resembles a Poisson random . or 6 you lose $1.49 Of the following. B. 5. variable is the number of: A. 4. D. The charity sells 4. .25 . A.50 $0. Find the expected winnings. 6 you lose $1.50 $1. $0.00 $0. or . A.000. 5. annual power failures at your residence.000 raffle tickets.00 $1.75 $1. If it rolls to a 1.50 $0. $0. B.00 $1. D. What is the expected value E(X) for this distribution? A. what is its expected net profit? A. C.50 $0. B. companies besides ESCO are bidding for a $900.00 and if it lands tails you lose $0. for Professor Smith's office hours on Monday afternoons.000 $0 55 The discrete random variable X is the number of students that show up . $0.000 $90.50. If it lands heads .00 54 Ephemeral Services Corporation (ESCO) knows that nine other .000 government contract. 1.5 2. B.0 .75 $1.53 A carnival has a game of chance: a fair coin is tossed. $100. C.000 -$10.2 1. Each company has an equal chance of being awarded the contract.000 in developing its bidding proposal.25 $0. D. D. If ESCO has already spent $100. C. B. How much should a ticket to play this game cost if the carnival wants to break even? A. The table below shows the probability distribution for X.0 1. you win $1. The table below shows the probability distribution for X.3 1. . C. C.40 . 1. C.1 1. D. What is the probability that at least 1 student comes to office hours on any given Monday? A. for Professor Smith's office hours on Monday afternoons. B. for Professor Smith's office hours on Monday afternoons.50 . B. What is the expected value E(X) for this distribution? A. D.9 .40 .60 57 The discrete random variable X is the number of students that show up . a bus stop. D. .56 The discrete random variable X is the number of students that show up .7 1.70 .30 .90 58 The discrete random variable X is the number of passengers waiting at .10 . What is the probability that fewer than 2 students come to office hours on any given Monday? A. The table below shows the probability distribution for X. The table below shows the probability distribution for X. B. trials to obtain n "successes" in a Bernoulli process. The "success" must be a desirable outcome. B. C. D. A. B. what is the expected value . A. C. B. 175 150 200 205 60 Which of the following characterizes a Bernoulli process? . A random experiment that has only two outcomes. 61 The binomial distribution describes the number of: . D. "successes" in n Bernoulli trials. A. D.59 Given the following probability distribution. "successes" or "failures" in a Bernoulli process. of the random variable X? A. The probability of "success" varies with each trial. C. 62 Which of the following is not a requirement of a binomial distribution? . B. trials to obtain the first "success" in a Bernoulli process. Either outcome has the same chance of occurrence. D. Constant probability of success Only two possible Bernoulli outcomes Fixed number of trials Equally likely outcomes . C. π = ¼ and 1 . The probability of "success" is: A.80 and 4. π = ½ and 1 . .π = ½. B. π = .π = 1. B. Binomial with n = 50.40 Binomial with n = 50. π = 1 and 1 . π = . C.75 .70 Binomial with n = 50. C.20 67 The expected value (mean) of a binomial variable is 15. trials is 20. A. D.00 and 1. .00 6. π = ½ and 1 . π = 0 and 1 . A.40.63 The binomial distribution is symmetrical when: .π = 1. A. D. B.π = 0.π = ½. D. π = 0 and 1 . The expected value and standard deviation of the variables are: A. B. D. 2.96 2.24 4. D. 65 Which distribution is most strongly right-skewed? .30 . π = 1 and 1 .50 .π = 0. C.π = ¾. π = ¼ and 1 .40 and 1. π = . C. B.25 . 64 The variance will reach a maximum in a binomial distribution when: .90 Binomial with n = 50. π = . C.00 and 1. The number of .π = ¾.10 66 A random variable is binomially distributed with n = 16 and π = . 1342 . What is the probability that Harry will get more than 2 hits? A. find the probability that the sample contains at least five Roman Catholics.3020 . D. working.4417 71 The probability that a visitor to an animal shelter will adopt a dog is .8131 . C. what is the probability that at least one dog will be adopted? A. C.68 If 90 percent of automobiles in Orange County have both headlights . a 20 percent chance .1869 69 In Quebec. Catholic religion. B.5639 .9619 70 Hardluck Harry has a batting average of . .6174 .0331 . Out of nine visits. . 20. . . B.7946 .e.3826 . at least seven will have both headlights working? A.8658 . what is the probability that in a sample of eight automobiles. C. B. D. In a random sample of eight Quebecois. . of a hit each time he's at bat).0050 .2055 . B. C..2362 .200 (i. A. D.9950 . D. 90 percent of the population subscribes to the Roman . Scouts for a rival baseball club secretly observe Harry's performance in 12 random times at bat. 72 Based on experience. headlight.3504 .0116 . none will have a burned-out headlight? A. . . C.6177 .9950 .9619 .1424 . D.0835 73 If 5 percent of automobiles in Oakland County have one burned-out .5987 . what is the probability that. what is the probability that fewer than 7 will be carrying backpacks? A. . If eight rings are sold today. B. .2001 . B. pregnancy test at a certain clinic are actually pregnant. backpack is . B. C. In a random sample of 12 women. provided the return occurs within two weeks. .0331 . 10 percent are returned. B.1872 74 Jankord Jewelers permits the return of their diamond wedding rings. what is the probability that at least 10 are pregnant? A.0639 . If 10 students are observed at random. C.3151 . D. 60 percent of the women who request a . D.70.2668 .1488 75 The probability that an Oxnard University student is carrying a . C. Typically.0196 . in a sample of 10 automobiles. D. what is the probability that fewer than three will be returned? A. D.25. . C. RAND()) =BINOM. =BINOM.0388 77 A random variable X is distributed binomially with n = 8 and π = 0. the probability for a claim during a year is 15 percent.25. D.70.5584 .680 1. 0.25? A. then the probability that there will be at least two claims during the year is equal to: A. RAND()) =BINOM. B. . RAND()) .2775 . If the binomial probability distribution is applicable. B.2362 .20. B. C. D. 16.296 78 Suppose X is binomially distributed with n = 12 and π = . 0) =BINOM. 16. .5615 . B.76 An insurance company is issuing 16 car insurance policies.INV(0. The .DIST(0.458 2.DIST(RAND(). . . C.25. probability that X will be less than or equal to 3 is: A.7946 .7161 . binomial random variable with parameters n = 16 and π = . . . D.25. 16.7638 79 Which Excel function would generate a single random X value for a . The standard deviation of the variable X is approximately: A. Suppose . C.INV(16.828 1. 9 percent. The probability that the network will be functioning correctly (at least one server is working) at a given time is: A. each with 90 percent . . What is the probability that fewer than two will be unlicensed? A.3670 . 2 percent of the stray dogs in Southfield are unlicensed. 97.2 percent. B. C. 72. 95.9 percent. C. 82 Historically. B. Its PDF is the same as its CDF when π = . the Southfield city animal control officer picks up seven stray dogs. D. 99.8681 . C. include: A.9921 . . D.0076 83 The domain of X in a Poisson probability distribution is discrete and can . B.50. D. Its CDF is skewed right when π < . reliability. D. A. 81 Which statement concerning the binomial distribution is correct? .80 A network has three independent file servers. Its PDF covers all integer values of X from 0 to n. B.50. C. any X value except zero. any real X value. Its CDF shows the probability of each value of X. .9 percent. any integer X value. any nonnegative integer X value. On a randomly chosen day. 1992 . .1523 87 On a Sunday in April. per hour. Find the probability that at least one major earthquake will occur within the next decade.7408 . .8913 . C. calls arrive at TicketMaster at a rate of 108 calls .0427 . D.7 fraudulent income tax returns . On a given Sunday in April. What is the probability of fewer than three calls in a randomly chosen minute? A.1005 . . per day. B.0919 . B.1494 . three times a decade in a certain California county.7306 85 On average.84 On Saturday morning. dog bite victims arrive at Carver Memorial . Hospital at a historical rate of 0. On a randomly chosen day. A. D. C.0875 .6 victim per day. C. B. D.0988 . .0 or above) occurs .0902 .9502 86 On average. D.2678 .1607 . an IRS auditor discovers 4. what is the probability that exactly two dog bite victims will arrive? A. C. what is the probability that she discovers fewer than two? A. a major earthquake (Richter scale 6. B.0518 . 44.2674 . the mean arrival rate is at least 30. B. A. What is .8795 . 91 The coefficient of variation for a Poisson distribution with λ = 5 is: . no more than one arrival can occur in a minute. D. 31. C. . the probability that exactly eight cars will arrive in the next two minutes? A. Poisson distribution if: A. .2 percent.9666 0.1 percent. C. B. 0.7 percent. 35. B.88 If tubing averages 16 defects per 100 meters. D. there is only one lane leading to the booth. C. what is the probability of . D.0349 0.1396 0.0005 90 Arrival of cars per minute at a toll booth may be characterized by the . the arrivals are independent.9 percent. 58. C. D. finding exactly 2 defects in a randomly chosen 10-meter piece of tubing? A.2584 89 Cars are arriving at a toll booth at a rate of four per minute. B.3422 . B. D. C.01 n = 80. 93 For which binomial distribution would a Poisson approximation be .10 n = 500.03 . A. π = 0. D. π = 0.08 n = 100. 26. π = 0. C. n = 35.2 percent.03 n = 200. C. π = 0. π = 0. unacceptable? A.15 n = 40.02 n = 50.03 n = 20.92 The coefficient of variation for a Poisson distribution with λ = 4 is: . n = 30.01 94 For which binomial distribution would a Poisson approximation be . 58. π = 0.4 percent. D. C. π = 0. π = 0. D.0 percent. n = 60. π = 0. π = 0.07 n = 95. acceptable? A. π = 0. B.02 n = 50. 50.20 95 For which binomial distribution would a Poisson approximation not be . π = 0. B. acceptable? A.9 percent. 35. B. 0053 . . If 3500 cars . . what is the approximate Poisson probability that fewer than two will contain errors? A. C. B. D. D.1038 . C. If 180 . 02 for Venal Enterprises. what is the approximate Poisson probability that 4 or fewer will be with stolen cards? A.0916 . purchase at a certain Target store is 0.1647 . are rented. . passengers take the flight.3452 .96 The true proportion of accounts receivable with some kind of error is . C. If 400 purchases are made in a given day.2275 .0004. C.2417 .0015 97 The probability that a rental car will be stolen is 0. D. . B.9372 .8335 98 The probability that a customer will use a stolen credit card to make a . D.0555 99 The probability that a ticket holder will miss a flight is .9923 . If an auditor randomly samples 200 accounts receivable. what is the approximate Poisson probability that 2 or fewer will be stolen? A.0076 .005. . what is the approximate Poisson probability that at least 2 will miss the flight? A.0628 .003. B. B.5918 .1465 . 100 The probability that a certain daily flight's departure from ORD to LAX . find . B. B. B. . C.4471 .3750 103 If X is a discrete uniform random variable ranging from one to eight.02.5000 . P(X ≥ 10). C.1666 . C. . . C.5 5. What is the approximate Poisson probability that it will be delayed fewer than 2 times? A. its mean is: A. Over six months.1771 101 If X is a discrete uniform random variable ranging from 0 to 12. this flight departs 180 times. D.1126 .6250 . find P(X < 6). . D.0 4.1257 . D. . A. A. D. is delayed is . 4.3028 .2500 102 If X is a discrete uniform random variable ranging from one to eight. B.2308 .7500 .0 5.5 . A.1681 .0. . the graduating class of 480 includes 96 guest . A sample of 10 students is selected at random to attend a dinner with the Board of Governors. B. . of .8319 . whom 27 are traveling on business. 18. its . D. A.0. 18. 19. B. C. B.3602 .3087 . 105 At Ersatz University. students from Latvia.6778 106 There are 90 passengers on a commuter flight from SFO to LAX.1209 .8791 . C. use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger. D. D. In a random sample of five passengers. C. mean is: A.5.104 If X is a discrete uniform random variable ranging from 12 to 24.3222 . 16.5. Use the binomial model to obtain the approximate hypergeometric probability that the sample contains at least three Latvian students. A.8263 .0533 . Assuming the doctors are assigned randomly to patients. B.7373 0. C. 0.0579 0.0397 . C. probability of at least two damaged flash drives in a sample of five taken from a shipment of 150 that contains 30 damaged flash drives. . B.0295 .5613 109 A clinic employs nine physicians. Five of the physicians are female. C.2322 . . 112 of 280 passengers on a particular DTW-LAX . In a random sample of eight passengers. flight used the e-ticket check-in kiosk to obtain boarding passes. Four patients arrive at once. B.2627 108 On a particular day.0808 . use the binomial model to find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.9421 0. D. A.2926 . D.107 Use the binomial model to find the approximate hypergeometric . what is the probability that all of the assigned physicians are female? A. D. . in humanities.0200 111 Ten percent of the corporate managers at Axolotl Industries majored .0656 . the probability of being called for an . What is the probability that the first such rejection occurs on the third Visa transaction? A. B.2410 . What is the expected number of managers to be interviewed until finding the first one with a humanities major? A. 15 20 10 17 113 When you send out a resume.5904 . D.0025 . B. rejected at a certain Target store because the transaction exceeds the customer's credit limit.110 There is a . . B.02 probability that a customer's Visa charge will be . interview is . D. C. D.4096 . C.4095 112 Ten percent of the corporate managers at Axolotl Industries majored . D. What is the probability that the first interview occurs on the fourth resume that you send out? A. C. B. . .8561 . What is the probability that the first humanities major is the fifth manager you meet? A.1024 .0192 . C.0247 . in humanities.20.0016 . C.02 probability that a customer's Visa charge will be .4000 .1362 . interview is .20. What is the probability that the first such rejection occurs within the first 20 Visa transactions? A.2410 . B. .20. D. What is the expected number of resumes you send out until you get the first interview? A.4538 117 There is a . C. B.02 probability that a customer's Visa charge will be .6723 . B. C. rejected at a certain Target store because the transaction exceeds the customer's credit limit. C.114 When you send out a resume. . 5 7 10 12 115 When you send out a resume. the probability of being called for an . D. rejected at a certain Target store because the transaction exceeds the customer's credit limit. B. the probability of being called for an . interview is . D.1024 . D. 10 20 50 98 .3324 . What is the expected number of Visa transactions until the first one is rejected? A. What is the probability that you get your first interview within the first five resumes that you send out? A.0016 116 There is a . what is the probability of obtaining . D. C. D. C. the number of successes in a sample of n trials. D.118 The geometric distribution best describes: .2228 121 If the probability of success is . A. . what is the probability of obtaining . the probability that no success will be obtained in a given Bernoulli trial.5781 . C.30.1681 . . the number of events in a given unit of time. B. B. the number of trials until the first success. the first success within the first three trials? A. the process of sampling without replacement. C.9976 . 120 If the probability of success is . the probability of success in a random experiment consisting of n independent trials. the first success within the first five trials? A. A.8319 . B.25.1406 . D. the probability that the first success will occur within a given number of trials. the probability of more than one success in the first n trials. B.0024 .4218 . 119 The CDF for the geometric distribution shows: . prices are independent random variables with standard deviations σX = 2.48 7. D. 33. The standard deviation of the overall project completion time is: A.73 5. C.77 15. μ3 = 17.0 14. 40. Their daily closing .24 124 A stock portfolio consists of two stocks X and Y.2 9. 32. B. σ2 = 4. C. The expected project completion time is: A. D. 123 A project has 3 independent stages that must be completed in .51 and σY = 5. sequence. B. 51. The time to complete each stage is a random variable. μ2 = 11. sequence. D. The standard deviations of the completion times for the stages are σ1 = 5. What is the standard deviation of the sum of the closing prices of these two stocks? A. 8. The time to complete each stage is a random variable. B.22. σ3 = 6.122 A project has three independent stages that must be completed in .79 .55 6. The expected times to complete the stages are μ1 = 23. 23. C. Their daily closing . 2 4 -10 -6 .55.68 126 The expected value of a random variable X is 140 and the standard .73 2.10 is: A.51 and σY2 = 5. B. prices are correlated random variables with variances σX2 = 3. 42 6. C. D. C.125 A stock portfolio consists of two stocks X and Y.22. B. 5.18 8. D. deviation is 2. deviation is 14. D.63 7. The standard deviation of the random variable Y = 3X .48 14 32 127 The expected value of a random variable X is 10 and the standard . and covariance σXY = -1. What is the standard deviation of the sum of the closing prices of these two stocks? A. C. The standard deviation of the random variable Y = 2X 10 is: A. B. A random variable is a function or rule that assigns a numerical value to each outcome in the sample space of a stochastic (chance) experiment. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-01 Define a discrete random variable. Topic: Discrete Distributions . A discrete random variable has a countable number of distinct values. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-01 Define a discrete random variable. TRUE Review definition of random variable. Topic: Discrete Distributions 2. TRUE Review definition of random variable.Chapter 06 Discrete Probability Distributions Answer Key True / False Questions 1. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-03 Define probability distribution. TRUE Review definition of expected value. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-02 Solve problems using expected value and variance. Topic: Discrete Distributions 5. but not both. TRUE Review definition of PDF and CDF. TRUE Review definition of discrete and continuous.3. Topic: Discrete Distributions 4. The expected value of a discrete random variable E(X) is the sum of all X values weighted by their respective probabilities. and CDF. A discrete distribution can be described by its probability density function (PDF) or by its cumulative distribution function (CDF). AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-01 Define a discrete random variable. PDF. Topic: Discrete Distributions . A random variable may be discrete or continuous. 6. To describe the number of blemishes per sheet of white bond paper, we would use a discrete uniform distribution. FALSE Not all X values would be equally likely (Poisson distribution would be better). AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel. Topic: Poisson Distribution 7. The outcomes for the sum of two dice can be described as a discrete uniform distribution. FALSE The sum of two uniforms is a triangular distribution, as shown in the textbook example. AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 06-04 Know the mean and variance of a uniform discrete model. Topic: Uniform Distribution 8. A discrete binomial distribution is skewed right when π > .50. FALSE Most outcomes would be on the right, so a longer left tail exists. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel. Topic: Binomial Distribution 9. When π = .70 the discrete binomial distribution is negatively skewed. TRUE Most outcomes would be on the right, so a longer left tail exists. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel. Topic: Binomial Distribution 10. The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space. TRUE Poisson describes events per unit of time. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel. Topic: Poisson Distribution 11. The Poisson distribution can be skewed either left or right, depending on λ. FALSE Poisson is always right-skewed. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel. Topic: Poisson Distribution 12. Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger. TRUE Although always right-skewed, the Poisson approaches a normal as the mean increases. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel. Topic: Poisson Distribution 13. As a rule of thumb, the Poisson distribution can be used to approximate a binomial distribution when n ≥ 20 and π ≤ .05. TRUE The Poisson is a better approximation to binomial when n is large and π is small. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-07 Use the Poisson approximation to the binomial (optional). Topic: Poisson Distribution 14. The hypergeometric distribution is skewed right. FALSE The hypergeometric is skewed right if s/N < .50 (and conversely). AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-08 Find hypergeometric probabilities using Excel. Topic: Hypergeometric Distribution 15. The hypergeometric distribution assumes that the probability of a success remains the same from one trial to the next. FALSE The point of the hypergeometric is that π is not constant. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-08 Find hypergeometric probabilities using Excel. Topic: Hypergeometric Distribution 16. The hypergeometric distribution is not applicable if sampling is done with replacement. TRUE The hypergeometric is used when there is no replacement in sampling from a finite population AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-08 Find hypergeometric probabilities using Excel. Topic: Hypergeometric Distribution 17. As a rule of thumb, the binomial distribution can be used to approximate the hypergeometric distribution whenever the population is at least 20 times as large as the sample. TRUE The rule is to use the approximation if n/N < .05. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-08 Find hypergeometric probabilities using Excel. Topic: Hypergeometric Distribution 18. An example of a geometric random variable is the number of pine trees with pine beetle infestation in a random sample of 15 pine trees in Colorado. FALSE This is a binomial experiment, assuming π is constant. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-09 Calculate geometric probabilities (optional). Topic: Geometric Distribution (Optional) 19. Calculating the probability of getting three aces in a hand of five cards dealt from a deck of 52 cards would require the use of a hypergeometric distribution. TRUE This is a hypergeometric experiment (no replacement). AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 06-08 Find hypergeometric probabilities using Excel. Topic: Hypergeometric Distribution 20. The Poisson distribution is appropriate to describe the number of babies born in a small hospital on a given day. TRUE Events per unit of time with no clear upper limit. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. Topic: Poisson Distribution Topic: Bernoulli Distribution 22. formulas. The Poisson distribution has only one parameter. TRUE Two outcomes (0 or 1).21. The gender of a randomly chosen unborn child is a Bernoulli event. TRUE Review Poisson model. formulas. or Excel. or Excel. The standard deviation of a Poisson random variable is the square root of its mean. AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. Topic: Poisson Distribution . AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-06 Find Poisson probabilities using tables. or Excel. Topic: Poisson Distribution 23. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-06 Find Poisson probabilities using tables. formulas. TRUE The one parameter is the mean. or Excel. formulas. The two outcomes (success. Topic: Poisson Distribution 25. TRUE The mean is another name for expected value.50. or Excel. AACSB: Analytic Blooms: Understand Difficulty: 1 Easy Learning Objective: 06-06 Find Poisson probabilities using tables. The expected value of a random variable is its mean. Topic: Discrete Distributions Multiple Choice Questions . formulas. FALSE This would be a Poisson (arrivals per unit of time). Topic: Bernoulli Distribution 26. FALSE The probability of success need not be . AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. Customer arrivals per unit of time would tend to follow a binomial distribution. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-02 Solve problems using expected value and variance. failure) in the Bernoulli model are equally likely.24. Topic: Discrete Distributions 28. PDF. C. A discrete probability distribution: A. continuous random variable. The number of male babies in a sample of 10 randomly chosen babies is a: A. AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 06-03 Define probability distribution. binomial random variable. Constant probability of success in n trials. D. can assume values between -1 and +1. and CDF. C. binary random variable. is independent of the parameters of the distribution. assigns a probability to each possible value of the random variable. Topic: Binomial Distribution . Poisson random variable. AACSB: Analytic Blooms: Understand Difficulty: 1 Easy Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. A discrete PDF assigns a probability to each X value. B. B. is a listing of all possible values of the random variable. D.27. AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 06-01 Define a discrete random variable. B. AACSB: Analytic Blooms: Apply .29. The number of births in a hospital on a given day The number of fives obtained in four rolls of a die The hourly earnings of a call center employee in Boston The number of applicants applying for a civil service job Someone's earnings would be more like a continuous measurement. The number of defects in a 4 × 8 sheet of plywood B. A discrete random variable: A. is usually uniformly distributed. B. The time until failure of a vehicle headlamp D. D. C. Which is not a discrete random variable? A. C. is best avoided if at all possible. AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 Define a discrete random variable. Which is a not a discrete random variable? A. can be treated as continuous when it has a large range of values. cannot be treated as continuous. D. The number of correct answers on a statistics exam Time is continuous. Review definitions of discrete distributions. Topic: Discrete Distributions 31. The number of female passengers who board a plane C. Topic: Discrete Distributions 30. Which statement is incorrect? A. B. The hypergeometric distribution is symmetric. Topic: Discrete Distributions 32. A hypergeometric is symmetric only if s/N = . The binomial distribution may be skewed left or right. Binomial Poisson Hypergeometric Geometric Geometric model describes the number of trials until the first success. The discrete uniform distribution is always symmetric. C. D. B. The random variable X is the number of shots it takes before you make the first free throw in basketball. Topic: Geometric Distribution (Optional) . Review characteristics of the distributions. AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 06-08 Find hypergeometric probabilities using Excel. what type of distribution does X follow? A. D. Topic: Hypergeometric Distribution 33.Difficulty: 1 Easy Learning Objective: 06-01 Define a discrete random variable. C. Assuming the probability of success (making a free throw) is constant from trial to trial.50. The Poisson distribution is always skewed right. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. C. Topic: Poisson Distribution . B. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. D. C. Topic: Binomial Distribution 35. Which distribution is most nearly appropriate to describe the number of fatalities in Texas in a given year due to poisonous snakebites? A. Binomial Poisson Hypergeometric Geometric n = 12 Bernoulli trials with fixed probability of success would be a binomial model. Binomial Poisson Hypergeometric Geometric Events per unit of time with no clear upper limit would resemble a Poisson distribution.34. Which probability model is most nearly appropriate to describe the number of burned-out fluorescent tubes in a classroom with 12 fluorescent tubes. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. assuming a constant probability of a burned-out tube? A. B. D. B. Which model would you use to describe the probability that a callcenter operator will make the first sale on the third call. D. Topic: Poisson Distribution . assuming a constant probability of making a sale? A. B. Topic: Geometric Distribution (Optional) 37. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.36. In a randomly chosen week. Binomial Poisson Hypergeometric Geometric Events per unit of time with no clear upper limit would resemble a Poisson distribution. D. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. C. C. which probability model would you use to describe the number of accidents at the intersection of two streets? A. Binomial Poisson Hypergeometric Geometric Geometric describes the number of trials to first success. Binomial Poisson Hypergeometric Geometric Events per unit of time with no clear upper limit would resemble a Poisson distribution. Topic: Poisson Distribution 39. C. B. D. Which model best describes the number of nonworking web URLs ("This page cannot be displayed") you encounter in a randomly chosen minute while surfing websites for Florida vacation rental condos? A. D. Which probability model would you use to describe the number of damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers? A. B. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. Topic: Hypergeometric Distribution .38. Poisson Hypergeometric Binomial Uniform Sampling (n = 4 printers) without replacement with known number of "successes" (s = 3 damaged printers) in the population (N = 28 printers). AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. C. A. C. Binomial Poisson Hypergeometric Geometric Events per unit of area with no clear upper limit would resemble a Poisson distribution. B. Which model best describes the number of incorrect fare quotations by a well-trained airline ticket agent between 2 p. Topic: Poisson Distribution . Which model best describes the number of blemishes per sheet of white bond paper? A. Topic: Poisson Distribution 41. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. B.40. C. and 3 p. D.m. on a particular Thursday. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. D. Binomial Poisson Hypergeometric Geometric Events per unit of time with no clear upper limit would resemble a Poisson distribution.m. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. D. To ensure quality. of which 4 are incorrect. In a random sample of 8 of these customer calls. B. C. D. Topic: Poisson Distribution . The number of people injured in rafting expeditions on the Colorado River on a randomly chosen Thursday in August is best described by which model? A. B. C. ticket agent Bob gives 40 fare quotations. which model best describes the number of incorrect quotations Bob will make? A. Binomial Poisson Hypergeometric Geometric Sampling (n = 8 calls selected) without replacement with known number of "successes" (s = 4 incorrect quotes) in the population (N = 40 quotes). customer calls for airline fare quotations are monitored at random. Topic: Hypergeometric Distribution 43. AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. Binomial Poisson Hypergeometric Geometric Independent events per unit of time with no clear upper limit would be Poisson.42. On a particular Thursday afternoon. Which model best describes the number of European tourists in the random sample? A. Binomial Poisson Hypergeometric Geometric Geometric distribution describes the number of trials until the first success. B. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. 40 Grand Canyon tourists enter a drawing for a free mule ride. Which model best describes the number of births in a hospital until the first twins are delivered? A. Binomial Poisson Hypergeometric Geometric Sampling (n = 5 tourists selected) without replacement with known number of "successes" (s = 10 Europeans) in the population (N = 40). Five entrants are selected at random to get the free mule ride.44. Topic: Hypergeometric Distribution 45. Ten of the entrants are European tourists. C. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. D. On a particular Thursday in August. D. Topic: Geometric Distribution (Optional) . C. B. Topic: Poisson Distribution 47.46. B. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. Binomial Poisson Hypergeometric Geometric Events per unit of time with no clear upper limit. C. D. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-10 Select an appropriate discrete probability distribution from problem context. C. D. On a randomly chosen Wednesday. Topic: Geometric Distribution (Optional) . which probability model would you use to describe the number of convenience store robberies in Los Angeles? A. Binomial Geometric Uniform Poisson Geometric distribution describes the number of trials until the first success. Which probability model would you use to describe the number of customers served at a certain California Pizza Kitchen until the first customer orders split pea soup? A. B. Binomial with n = 200. π = . Poisson with λ = 25. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-08 Find hypergeometric probabilities using Excel. Topic: Hypergeometric Distribution 49. Of the following. or Excel. Which distribution has a mean of 5? A. face cards in a bridge hand of 13 cards. defective CDs in a spool containing 15 CDs. The hypergeometric mean is ns/N = (10) (50)/100 = 5. Independent arrivals per unit of time with no clear upper limit would be Poisson. C.48. n = 10. annual power failures at your residence. Topic: Poisson Distribution . formulas. C. AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-06 Find Poisson probabilities using tables. heads in 200 flips of a fair coin. s = 50 Review model parameters.05 Hypergeometric with N = 100. B. the one that most resembles a Poisson random variable is the number of: A. B. D. C. A charity raffle prize is $1.00 E(X) = (3/6) × $2 + (3/6) × (-$1) = $0.50 $3. A die is rolled.00 Expected winning is (1/4000) × $1000 = $0. Find the expected winnings. 2.25 $0.000.50 $0.50. or 6 you lose $1. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-02 Solve problems using expected value and variance. At what ticket price would a ticket buyer expect to break even? A. D. Topic: Discrete Distributions . $0. C.000 raffle tickets. Topic: Discrete Distributions 51.50 $1. The charity sells 4. or 3 you win $2.00 $1. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-02 Solve problems using expected value and variance. $0. If it rolls to a 1. If it rolls to a 4. 5. B.25.75 $1.50. One winner will be selected at random. A. D. B. 25 = $0. A carnival has a game of chance: a fair coin is tossed. If it comes up 3. B.75 $1.50) = $0. A.5) × (-$. 4.50 . AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-02 Solve problems using expected value and variance. C. If it comes up 1 or 2 you win $2. If it lands heads you win $1. Topic: Discrete Distributions 53. 5. $0.50 $0. B.00 E(X) = (.5) × $1 + (. C.50.25. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-02 Solve problems using expected value and variance.$0.00 $0.$0.00 and if it lands tails you lose $0. Find the expected winnings. A fair die is rolled. or 6 you lose $1.00 $1. D.50 $0. D. How much should a ticket to play this game cost if the carnival wants to break even? A. Topic: Discrete Distributions .6667 = 0. $0.52.25 E(X) = (2/6) × $2 + (4/6) × (-$1) = $0.25 $0.6667 . 5 2. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-02 Solve problems using expected value and variance.0 For each X. D. B. The table below shows the probability distribution for X. Each company has an equal chance of being awarded the contract. Topic: Discrete Distributions . What is the expected value E(X) for this distribution? A. $100. C. what is its expected net profit? A.000 in developing its bidding proposal.000. ESCO only can expect to cover its sunk cost (no profit).000 $90.54. D.000 = $100. Topic: Discrete Distributions 55.2 1. The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. B. Ephemeral Services Corporation (ESCO) knows that nine other companies besides ESCO are bidding for a $900. If ESCO has already spent $100.0 1.000 $0 E(X) = (1/9) × $900. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-02 Solve problems using expected value and variance. multiply X time P(X) and sum the values.000 government contract. C.000 -$10. 1. 40 . AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-02 Solve problems using expected value and variance. AACSB: Analytic Blooms: Apply .70 .70. C. Topic: Discrete Distributions 57. B.60 P(X ≥ 1) = 1 .90 P(X < 2) = P(X = 0) + P(X = 1) = .56.40 = . The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. . The table below shows the probability distribution for X. The table below shows the probability distribution for X.60. What is the probability that fewer than 2 students come to office hours on any given Monday? A.P(X = 0) = 1 .30 .10 . What is the probability that at least 1 student comes to office hours on any given Monday? A. D. .50 .30 = .40 + . The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons.40 . B. D. C.. Topic: Discrete Distributions 58. C.Difficulty: 1 Easy Learning Objective: 06-02 Solve problems using expected value and variance. D. Topic: Discrete Distributions .7 1. multiply X time P(X) and sum the values. What is the expected value E(X) for this distribution? A.3 1. The table below shows the probability distribution for X. The discrete random variable X is the number of passengers waiting at a bus stop.9 For each X. B.1 1. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-02 Solve problems using expected value and variance. 1. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-05 Find binomial probabilities using tables. The "success" must be a desirable outcome.59. C. B. D. or Excel. Topic: Discrete Distributions 60. 175 150 200 205 For each X. Topic: Bernoulli Distribution . C. Review characteristics of the Bernoulli process. what is the expected value of the random variable X? A. The probability of "success" varies with each trial. Given the following probability distribution. Which of the following characterizes a Bernoulli process? A. multiply X time P(X) and sum the values. A random experiment that has only two outcomes. formulas. Either outcome has the same chance of occurrence. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-02 Solve problems using expected value and variance. B. D. "successes" in n Bernoulli trials. D. "successes" or "failures" in a Bernoulli process. trials to obtain n "successes" in a Bernoulli process. Review characteristics of the binomial distribution. formulas. B. or Excel.61. B. C. Constant probability of success Only two possible Bernoulli outcomes Fixed number of trials Equally likely outcomes Review characteristics of the binomial distribution. Topic: Binomial Distribution 62. formulas. The binomial distribution describes the number of: A. trials to obtain the first "success" in a Bernoulli process. Which of the following is not a requirement of a binomial distribution? A. or Excel. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-05 Find binomial probabilities using tables. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. C. Topic: Binomial Distribution . D. The binomial distribution is symmetrical when: A.π = ½. 50. The variance will reach a maximum in a binomial distribution when: A. π = 1 and 1 .70 . B.π = 1. Review formula for the binomial distribution standard deviation. Topic: Binomial Distribution 65. Review characteristics of the binomial distribution. B.π = ½. π = 0 and 1 . formulas.40 . D. formulas. π = ¼ and 1 .π = ¾.90 . or Excel. C. AACSB: Analytic Blooms: Understand . D. D. C. AACSB: Analytic Blooms: Remember Difficulty: 3 Hard Learning Objective: 06-05 Find binomial probabilities using tables. π = ¼ and 1 . or Excel.π = 0. 50. C. π = ½ and 1 . π = 0 and 1 . π = 1 and 1 . Binomial Binomial Binomial Binomial with with with with n n n n = = = = 50.π = 1.63. Which distribution is most strongly right-skewed? A. π π π π = = = = . B. π = ½ and 1 . 50. Topic: Binomial Distribution 64.π = 0. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables.π = ¾.10 Review characteristics of the binomial distribution. 20 Review characteristics of the binomial distribution. B.24 4. C.00 1. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables.75 .00 4. A random variable is binomially distributed with n = 16 and π = .50 . or Excel. formulas. formulas.40. B. or Excel. AACSB: Analytic Blooms: Understand Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. The probability of "success" is: A.25 . . The expected value (mean) of a binomial variable is 15. The expected value and standard deviation of the variables are: A. The number of trials is 20. or Excel.Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. Topic: Binomial Distribution 67.30 Set E(X) = nπ = (20)π = 15 and solve for π. D.96 1. Topic: Binomial Distribution 66. D. Topic: Binomial Distribution .00 and and and and 1.40 2. formulas.80 6. C. 2. 8131. . B.8131 . AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. Topic: Binomial Distribution .90.6174 .1869 Use Appendix A with n = 8 and π = .99498.1) = . what is the probability that in a sample of eight automobiles. C.90 to find P(X ≥ 7) or else use the Excel function =1-BINOM.8. Topic: Binomial Distribution 69.1) = .9619 Use Appendix A with n = 8 and π = . D. formulas. A. In a random sample of eight Quebecois. D. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables.9950 .68. . 90 percent of the population subscribes to the Roman Catholic religion. or Excel.0331 . at least seven will have both headlights working? A.. If 90 percent of automobiles in Orange County have both headlights working. formulas.DIST(4. C.8..DIST(6.0050 . In Quebec.3826 . or Excel.90. find the probability that the sample contains at least five Roman Catholics. B.90 to find P(X ≥ 5) or else use the Excel function =1-BINOM. The probability that a visitor to an animal shelter will adopt a dog is . . B. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. Topic: Binomial Distribution 71.3020 .7946 . Out of nine visits.2362 . D. Scouts for a rival baseball club secretly observe Harry's performance in 12 random times at bat.20.200 (i. or Excel.e.12. C. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables..20 to find P(X ≥ 3) or else use the Excel function =1-BINOM.44165.9..865778.4417 Use Appendix A with n = 12 and π = . What is the probability that Harry will get more than 2 hits? A.70. Topic: Binomial Distribution . Hardluck Harry has a batting average of .. or Excel.1342 Use Appendix A with n = 9 and π = . formulas.1) = .8658 .20.2055 . formulas.DIST(0. D. .20 to find P(X ≥ 1) or else use the Excel function =1-BINOM.5639 . B. C. what is the probability that at least one dog will be adopted? A.1) = . 20.DIST(2. a 20 percent chance of a hit each time he's at bat). Based on experience.12.60.3151 .08344.0116 .05 find P(X = 0) or else use the Excel function =BINOM. AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-05 Find binomial probabilities using tables.1424 . or Excel. what is the probability that at least 10 are pregnant? A. In a random sample of 12 women. D.DIST(9.0) = . If 5 percent of automobiles in Oakland County have one burned-out headlight.0835 Use Appendix A with n = 12 and π = .0639 ..DIST(0. 60 percent of the women who request a pregnancy test at a certain clinic are actually pregnant.60 to find P(X ≥ 10) or else use the Excel function =1-BINOM.0196 . or Excel.10. D.5987 . formulas. in a sample of 10 automobiles. C. C. .05. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. none will have a burned-out headlight? A. formulas. B. .. what is the probability that. Topic: Binomial Distribution . B.72.59874.1872 Use Appendix A with n = 10 and π = .1) = . Topic: Binomial Distribution 73. Topic: Binomial Distribution 75.70 to find P(X < 7) or else use the Excel function =BINOM. C.10. what is the probability that fewer than 7 will be carrying backpacks? A. or Excel. Jankord Jewelers permits the return of their diamond wedding rings.96191. 10 percent are returned.2001 . If 10 students are observed at random.8.0331 . B.DIST(2.6177 ..1.1488 Use Appendix A with n = 8 and π = .70.74. .1) = .10 to find P(X < 3) or else use the Excel function =BINOM. The probability that an Oxnard University student is carrying a backpack is .DIST(6.9950 . D.1) = . . what is the probability that fewer than three will be returned? A. If eight rings are sold today.. Topic: Binomial Distribution . D. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. Typically.3504 . formulas. C.9619 . or Excel. provided the return occurs within two weeks. B.2668 Use Appendix A with n = 10 and π = .35039. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables.7. formulas. . B.5615 . C.680 1.828 1.70. The standard deviation of the variable X is approximately: A. 0. AACSB: Analytic Blooms: Understand Difficulty: 1 Easy Learning Objective: 06-05 Find binomial probabilities using tables. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables.15.458 2.7161.296 Use the formula for the binomial standard deviation.7161 . Suppose the probability for a claim during a year is 15 percent. If the binomial probability distribution is applicable.0388 Use Appendix A with n = 16 and π = . D. formulas.1) = .DIST(1.16. then the probability that there will be at least two claims during the year is equal to: A. Topic: Binomial Distribution . D. or Excel. A random variable X is distributed binomially with n = 8 and π = 0. Topic: Binomial Distribution 77. formulas.2775 . An insurance company is issuing 16 car insurance policies. C. .15 to find P(X ≥ 2) or else use the Excel function =1-BINOM.76. B. or Excel. 1) = . .INV(16. . Topic: Binomial Distribution 79. 16. 0) =BINOM..20. formulas. RAND()) =BINOM.25. D.2. =BINOM.DIST(RAND().25. B. . D. B. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. or Excel.25. 16. RAND()) =BINOM. Topic: Binomial Distribution .78. The probability that X will be less than or equal to 3 is: A. .5584 .7638 Use Appendix A with n = 12 and π = .25. or Excel.DIST(3. formulas. 16. .25? A. Suppose X is binomially distributed with n = 12 and π = . RAND()) This is the Excel 2010 function for the inverse of a binomial. Which Excel function would generate a single random X value for a binomial random variable with parameters n = 16 and π = . AACSB: Technology Blooms: Remember Difficulty: 3 Hard Learning Objective: 06-05 Find binomial probabilities using tables.79457.12.DIST(0. C.2362 . C.INV(0.7946 .20 to find P(X ≤ 3) or else use the Excel function =BINOM. .. Its CDF is skewed right when π < . Review definitions of the binomial distribution.9 72. Its PDF covers all integer values of X from 0 to n. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-03 Define probability distribution. Topic: Binomial Distribution 81..50. B.50. D. percent. C. Topic: Binomial Distribution . The binomial domain is X = 0. each with 90 percent reliability. 1.2 95.9 97. Its PDF is the same as its CDF when π = . Which statement concerning the binomial distribution is correct? A. Use Appendix A with n = 3 and π = . D. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-05 Find binomial probabilities using tables.90. . percent. formulas. B. and CDF. 99. n. Its CDF shows the probability of each value of X.9 percent. PDF. The probability that the network will be functioning correctly (at least one server is working) at a given time is: A. A network has three independent file servers. C. percent.80. or Excel. formulas. … (no upper limit). any real X value. the Southfield city animal control officer picks up seven stray dogs. Topic: Poisson Distribution .9921 . AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-06 Find Poisson probabilities using tables. X = 0. C. D. or Excel. B. For a Poisson random variable.3670 . . B. 2 percent of the stray dogs in Southfield are unlicensed.02. C. formulas. The domain of X in a Poisson probability distribution is discrete and can include: A.82. Topic: Binomial Distribution 83. 1. Historically. or Excel. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-05 Find binomial probabilities using tables. 2. D. What is the probability that fewer than two will be unlicensed? A. any integer X value.0076 Use Appendix A with n = 7 and π = .8681 . any nonnegative integer X value. any X value except zero. On a randomly chosen day. . or Excel. D. On Saturday morning. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-06 Find Poisson probabilities using tables. Topic: Poisson Distribution 85.7306 Use Appendix B with λ = 108/60 = 1. Topic: Poisson Distribution . calls arrive at TicketMaster at a rate of 108 calls per hour. C. D.2678 . Find the probability that at least one major earthquake will occur within the next decade. A. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-06 Find Poisson probabilities using tables.0. C. B. B.7408 .1607 .8913 . a major earthquake (Richter scale 6. or Excel.84. formulas.8. On average.0 or above) occurs three times a decade in a certain California county.1494 . .9502 Use Appendix B with λ = 3. formulas. What is the probability of fewer than three calls in a randomly chosen minute? A.1992 . 0988 .1523 Use Appendix B with λ = 4. On a given Sunday in April. On average. B.7. or Excel. D. B. .6. formulas. dog bite victims arrive at Carver Memorial Hospital at a historical rate of 0.1005 . what is the probability that exactly two dog bite victims will arrive? A. formulas. On a Sunday in April. On a randomly chosen day. D.0875 .0902 .86. C. Topic: Poisson Distribution . . C. what is the probability that she discovers fewer than two? A. Topic: Poisson Distribution 87. an IRS auditor discovers 4.0427 .0919 Use Appendix B with λ = 0. or Excel. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-06 Find Poisson probabilities using tables.7 fraudulent income tax returns per day.0518 .6 victim per day. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-06 Find Poisson probabilities using tables. formulas. or Excel. C.2674 . D. Topic: Poisson Distribution 89. .0.2584 Use Appendix B with λ = 16/10 = 1. C. B. 0.3422 . Cars are arriving at a toll booth at a rate of four per minute. Topic: Poisson Distribution . What is the probability that exactly eight cars will arrive in the next two minutes? A.0349 0. B.9666 0.6.0005 Use Appendix B with λ = 4. what is the probability of finding exactly 2 defects in a randomly chosen 10-meter piece of tubing? A. formulas.88. If tubing averages 16 defects per 100 meters. or Excel. D.8795 .1396 0. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-06 Find Poisson probabilities using tables. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-06 Find Poisson probabilities using tables. 1 percent. percent. formulas. The coefficient of variation for a Poisson distribution with λ = 5 is: A. Topic: Poisson Distribution 91. or Excel. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-06 Find Poisson probabilities using tables. there is only one lane leading to the booth. Arrival of cars per minute at a toll booth may be characterized by the Poisson distribution if: A. the mean arrival rate is at least 30. the arrivals are independent. Use the coefficient of variation with standard deviation equal to the square root of the mean.7 31. Events per unit of time with no clear upper limit. D. C. percent. formulas. or Excel.9 44. no more than one arrival can occur in a minute. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-06 Find Poisson probabilities using tables. B. C. B. D.2 58. 35. percent.90. Topic: Poisson Distribution . D. D. B. percent. n = 30.10 n = 500. The coefficient of variation for a Poisson distribution with λ = 4 is: A. 35. Topic: Poisson Distribution . Topic: Poisson Distribution 93.05. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-07 Use the Poisson approximation to the binomial (optional). The Poisson standard deviation is the square root of the mean. percent.02 n = 50. π = 0.92. For which binomial distribution would a Poisson approximation be unacceptable? A. formulas. π = 0. B. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-06 Find Poisson probabilities using tables.9 50. or Excel.2 58. π = 0. π = 0.4 percent.03 n = 200. C.01 We want n ≥ 20 and π ≤ .0 26. C. percent. C.08 n = 100.05 for an acceptable Poisson approximation. n n n n = = = = 35.20 We want n ≥ 20 and π ≤ . π = 0.03 We want n ≥ 20 and π ≤ . For which binomial distribution would a Poisson approximation be acceptable? A. Topic: Poisson Distribution 95.02 0. 80. B. 50. 95. D. Topic: Poisson Distribution .03 n = 20. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-07 Use the Poisson approximation to the binomial (optional).05 for an acceptable Poisson approximation. D. B. π π π π = = = = 0.01 0. π = 0.07 0. n = 60. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-07 Use the Poisson approximation to the binomial (optional). For which binomial distribution would a Poisson approximation not be acceptable? A. π = 0.15 n = 40. C. π = 0.94. 8335 Since n ≥ 20 and π ≤ .DIST(1. .1038 .1) = .02 for Venal Enterprises.1. what is the approximate Poisson probability that fewer than two will contain errors? A.96.02) = 4. D.2417 .1465 . AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-07 Use the Poisson approximation to the binomial (optional).0 and use Appendix B to find P(X ≤ 1).1) = .0916 .0015 Since n ≥ 20 and π ≤ .5918 .4.0004) = 1. Topic: Poisson Distribution .8335. D. C.0.09158.4 and use Appendix B to find P(X ≤ 2).4. If an auditor randomly samples 200 accounts receivable. B.DIST(2. If 3500 cars are rented. or else use the Excel cumulative distribution function =POISSON. C. or else use the Excel cumulative distribution function =POISSON. what is the approximate Poisson probability that 2 or fewer will be stolen? A. . The true proportion of accounts receivable with some kind of error is . B.05 we can set λ = nπ = (200)(. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-07 Use the Poisson approximation to the binomial (optional).3452 . The probability that a rental car will be stolen is 0.05 we can set λ = nπ = (3500)(. Topic: Poisson Distribution 97.0004. B.9923. C.9372 .0076 .DIST(1. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-07 Use the Poisson approximation to the binomial (optional).05 we can set λ = nπ = (.1647 .0.9923 . If 180 passengers take the flight. D.005.98. Topic: Poisson Distribution .0628 . B. The probability that a customer will use a stolen credit card to make a purchase at a certain Target store is 0.05 we can set λ = nπ = (400)(.1) = .2 and use Appendix B. If 400 purchases are made in a given day.005)(180) = 0. what is the approximate Poisson probability that 4 or fewer will be with stolen cards? A.1) = .003.0053 . AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-07 Use the Poisson approximation to the binomial (optional).0555 Since n ≥ 20 and π ≤ .003*400. The probability that a ticket holder will miss a flight is .DIST(4. Topic: Poisson Distribution 99. C.9 and use Appendix B to find P(X ≥ 2). or else use the Excel cumulative distribution function = 1-POISSON.003) = 1. what is the approximate Poisson probability that at least 2 will miss the flight? A. . or else use the Excel cumulative distribution function =POISSON. D. .9.2275 Since n ≥ 20 and π ≤ ..2275. C. Topic: Poisson Distribution 101. A.6. The probability that a certain daily flight's departure from ORD to LAX is delayed is . D.12569. What is the approximate Poisson probability that it will be delayed fewer than 2 times? A.4471 . .2500 3 out of 13 outcomes (don't forget to count 0 as an outcome).05 we can set λ = nπ = (180)(.3. .DIST(1. D. B.1771 Since n ≥ 20 and π ≤ . Topic: Uniform Distribution .1257 .1666 . C. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-07 Use the Poisson approximation to the binomial (optional).3028 .2308 . find P(X ≥ 10). Over six months. If X is a discrete uniform random variable ranging from 0 to 12. this flight departs 180 times.6 and use Appendix B to find P(X ≤ 1) or else use the Excel cumulative distribution function =POISSON.100.1) = .02) = 3.1126 . AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-04 Know the mean and variance of a uniform discrete model. B.02. find P(X < 6).5000 . its mean is: A. D. D. Topic: Uniform Distribution .5 The mean is halfway between the lower and upper limits 1 and 8. C.102.0 4. Topic: Uniform Distribution 103.5 5. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-04 Know the mean and variance of a uniform discrete model. B. . B. C. 4.6250 . A. If X is a discrete uniform random variable ranging from one to eight.7500 .3750 We count five out of eight outcomes that meet this requirement. If X is a discrete uniform random variable ranging from one to eight. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-04 Know the mean and variance of a uniform discrete model.0 5. 1209 .20 to find P(X ≥ 3). D. If X is a discrete uniform random variable ranging from 12 to 24. its mean is: A.0. 18. Topic: Uniform Distribution 105. Topic: Hypergeometric Distribution . 18.5. 19. B. C. At Ersatz University. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-08 Find hypergeometric probabilities using Excel. . A sample of 10 students is selected at random to attend a dinner with the Board of Governors. 16.5. AACSB: Analytic Blooms: Remember Difficulty: 1 Easy Learning Objective: 06-04 Know the mean and variance of a uniform discrete model. B.0. Use the binomial model to obtain the approximate hypergeometric probability that the sample contains at least three Latvian students.3222 . A.05 we can use Appendix A with n = 10 and π = 96/480 = . D. The mean is halfway between the lower and upper limits 12 and 24.6778 Since n/N < . the graduating class of 480 includes 96 guest students from Latvia.104.8791 . C. 05 we can use Appendix A with n = 5 and π = 27/90 = .0579 0. 30 to find P(X ≥ 1). D. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-08 Find hypergeometric probabilities using Excel. . There are 90 passengers on a commuter flight from SFO to LAX. C. 0.7373 0. C.3087 . AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-08 Find hypergeometric probabilities using Excel.2627 Since n/N < . A. Topic: Hypergeometric Distribution .05 we can use Appendix A with n = 5 and π = 30/150 = .3602 .20 to find P(X ≥ 2). A. Use the binomial model to find the approximate hypergeometric probability of at least two damaged flash drives in a sample of five taken from a shipment of 150 that contains 30 damaged flash drives. of whom 27 are traveling on business. B. In a random sample of five passengers. Topic: Hypergeometric Distribution 107.106.9421 0.8319 Since n/N < .1681 . use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger. B. D. 0) = . what is the probability that all of the assigned physicians are female? A.8263 .0808 . s = 5.2322 . Assuming the doctors are assigned randomly to patients.4. B. A clinic employs nine physicians. Topic: Hypergeometric Distribution 109.444) so use the hypergeometric formula with x = 4.40 to find P(X = 4). C. n = 4. C. N = 9 or use the Excel function =HYPGEOM. 112 of 280 passengers on a particular DTW-LAX flight used the e-ticket check-in kiosk to obtain boarding passes. D. Topic: Hypergeometric Distribution . AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-08 Find hypergeometric probabilities using Excel.03938.0533 You can't use the binomial approximation because we have sampled more than 5% of the population (n/N = 4/9 = . On a particular day.0397 . AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-08 Find hypergeometric probabilities using Excel.108.5613 Since n/N < . Five of the physicians are female.5.0295 . .2926 .DIST(4. A. Four patients arrive at once. B.9. D. In a random sample of eight passengers. .05 we can use Appendix A with n = 8 and π = 112/280 = . use the binomial model to find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes. D.019208.0025 .0247 .8561 .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. There is a .6561) = .90)4 = .98)2 = . C.02 to find P(X = 3) = . C..10 to find P(X = 5) = . AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-09 Calculate geometric probabilities (optional).9604) = . What is the probability that the first such rejection occurs on the third Visa transaction? A.10(. What is the probability that the first humanities major is the fifth manager you meet? A. B.06561. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-09 Calculate geometric probabilities (optional).02)3-1 = . Topic: Geometric Distribution (Optional) 111. D. Ten percent of the corporate managers at Axolotl Industries majored in humanities.0656 .5904 .02(.110.02(1 . . Topic: Geometric Distribution (Optional) .10(1 .02(. B. .0200 Use the formulas for the geometric PDF (not the CDF) with π = .4095 Use the formulas for the geometric PDF (not the CDF) with π = .10(.10)5-1 = ..0192 . 20 to find P(X = 4) = . AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-09 Calculate geometric probabilities (optional).20)4-1 = .10) = 10.0016 Use the formulas for the geometric PDF (not the CDF) with π = . What is the probability that the first interview occurs on the fourth resume that you send out? A. Topic: Geometric Distribution (Optional) .20.20(. Ten percent of the corporate managers at Axolotl Industries majored in humanities. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-09 Calculate geometric probabilities (optional)..1024. D. Topic: Geometric Distribution (Optional) 113.1024 .2410 . 15 20 10 17 The geometric mean is 1/π = 1/(. C. . B. C.20(. D.512) = . the probability of being called for an interview is .20(1 . What is the expected number of managers to be interviewed until finding the first one with a humanities major? A.4096 . When you send out a resume. B.112.80)3 = . 6723 . C.1024 .114. B.32678 = . Topic: Geometric Distribution (Optional) 115. .(. 5 7 10 12 The geometric mean is 1/π = 1/(.67232. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-09 Calculate geometric probabilities (optional).20) = 5. D. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-09 Calculate geometric probabilities (optional). When you send out a resume. What is the expected number of resumes you send out until you get the first interview? A..20. C.80)5 = 1 . What is the probability that you get your first interview within the first five resumes that you send out? A.0016 Use the formulas for the geometric CDF (not the PDF) with π = . the probability of being called for an interview is . D. B.20 to find P(X ≤ 5) = 1 -(1-. Topic: Geometric Distribution (Optional) . When you send out a resume.2410 .20. the probability of being called for an interview is .20)5 = = 1 . B. What is the expected number of Visa transactions until the first one is rejected? A..116.4538 Use the formulas for the geometric CDF (not the PDF) with π = .3324 .02) = 50.3324.1362 . AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-09 Calculate geometric probabilities (optional).6676 = . AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-09 Calculate geometric probabilities (optional).02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. Topic: Geometric Distribution (Optional) . B. D. D.98)20 = 1 . 10 20 50 98 The geometric mean is 1/π = 1/(. What is the probability that the first such rejection occurs within the first 20 Visa transactions? A.4000 . Topic: Geometric Distribution (Optional) 117. .02 to find P(X ≤ 20) = 1 -(1-.02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. There is a . C.(.02)20 = = 1 . There is a . C. B. D. Review the definition of geometric distribution. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-09 Calculate geometric probabilities (optional). the number of trials until the first success. the process of sampling without replacement. the probability that the first success will occur within a given number of trials. The geometric distribution best describes: A. the probability that no success will be obtained in a given Bernoulli trial. Topic: Geometric Distribution (Optional) 119. C. AACSB: Analytic Blooms: Remember Difficulty: 2 Medium Learning Objective: 06-09 Calculate geometric probabilities (optional). Topic: Geometric Distribution (Optional) .118. B. the number of events in a given unit of time. C. the number of successes in a sample of n trials. the probability of more than one success in the first n trials. The CDF for the geometric distribution shows: A. the probability of success in a random experiment consisting of n independent trials. D. Review the definition of geometric distribution. 25.1681 .30.16807 = . Topic: Geometric Distribution (Optional) . what is the probability of obtaining the first success within the first three trials? A.9976 Use the formulas for the geometric CDF (not the PDF) with π = . C.1406 .0024 .578125.2228 Use the formulas for the geometric CDF (not the PDF) with π = .421875 = . . AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-09 Calculate geometric probabilities (optional).120.75)3 = 1 .30)5 = 1 . If the probability of success is .30 to find P(X ≤ 5) = 1 -(1-.8319 . D. B.25)3 = 1 . Topic: Geometric Distribution (Optional) 121.(... B.(. D.4218 . If the probability of success is . AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-09 Calculate geometric probabilities (optional).70)5 = 1 .83193. C. what is the probability of obtaining the first success within the first five trials? A. .25 to find P(X ≤ 3) = 1 -(1-.5781 . 8. 51. σ32 = 36. Be careful . μ2 = 11. B. μ3 = 17.2 9. D. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-11 Apply rules for transformations of random variables (optional). σ3 = 6. The expected times to complete the stages are μ1 = 23. σ2 = 4. then add them and take the square root of the sum. The means can be summed because the stages are independent.122.the standard deviations cannot be summed.77 15. The standard deviations of the completion times for the stages are σ1 = 5. C. 32. A project has three independent stages that must be completed in sequence. 23. You have to square the standard deviations to get the variances σ12 = 25. The time to complete each stage is a random variable. The standard deviation of the overall project completion time is: A. B. D. Topic: Transformations of Random Variables (Optional) . Topic: Transformations of Random Variables (Optional) 123.0 14. A project has 3 independent stages that must be completed in sequence.24 The variances can be summed because the stages are independent (Rule 4). AACSB: Analytic Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-11 Apply rules for transformations of random variables (optional). σ22 = 16. The expected project completion time is: A. The time to complete each stage is a random variable. C. 40. 63 7.18]1/2 = 2.18 8. Be careful .22. D.55. Their daily closing prices are correlated random variables with variances σX2 = 3.2484. A stock portfolio consists of two stocks X and Y. B. What is the standard deviation of the sum of the closing prices of these two stocks? A. A stock portfolio consists of two stocks X and Y.22.73 2.68 Use the formula for the variance of correlated (nonindependent) events.51 + 5. AACSB: Analytic Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-11 Apply rules for transformations of random variables (optional).22 .55 6. You have to square the standard deviations to get the variances σX2 = 6.79 The variances can be summed because the stages are independent (Rule 4). . What is the standard deviation of the sum of the closing prices of these two stocks? A. Topic: Transformations of Random Variables (Optional) 125.51 and σY = 5. We sum the variances and covariance. Their daily closing prices are independent random variables with standard deviations σX = 2.73 5. then add them and take the square root of the sum.3001 and σY2 = 27.51 and σY2 = 5. and then take the square root: σX+Y = [σX2 + σY2 + σXY ]1/2 = [3.48 7. 5. D. C. and covariance σXY = -1. B.the standard deviations cannot be summed. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-11 Apply rules for transformations of random variables (optional).124.67955. 33.55]1/2 = [7. C.1. B. The standard deviation of the random variable Y = 3X . B.48 14 32 Use the rule for functions of a random variable (Rule 2) to get σY = 3σX = (3)(14) = 42.10 is: A. 2 4 -10 -6 Use the rule for functions of a random variable (Rule 2) to get σY = 2σX = (2)(2) = 4.10 is: A. The standard deviation of the random variable Y = 2X . The constant -10 merely shifts the distribution and has no effect on the standard deviation. The mean of Y is not requested. Topic: Transformations of Random Variables (Optional) 127. The constant -10 merely shifts the distribution and has no effect on the standard deviation.Topic: Transformations of Random Variables (Optional) 126. C. D. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-11 Apply rules for transformations of random variables (optional). C. The expected value of a random variable X is 10 and the standard deviation is 2. 42 6. The expected value of a random variable X is 140 and the standard deviation is 14. Topic: Transformations of Random Variables (Optional) . D. AACSB: Analytic Blooms: Apply Difficulty: 3 Hard Learning Objective: 06-11 Apply rules for transformations of random variables (optional). The mean of Y is not requested.