1. Shapiro, Director of Human Resources, is exploring employee absenteeism at Plain Power Plant.An analysis of personnel records indicated that 20% of all plant employees are absent excessively. This is an example of assigning probabilities by the ________________ method. 2. A die and a coin are tossed at the same time. Answer the following questions: a. Are these two experiments independent? Why? b. What is the sample space for the each experiment? What is the combined sample space? c. What is the probability that the die will show an odd number and the coin will land on head? d. What is the probability that the die will not show number “4”? 3. For each question below, determine True or False: a. If a simple random sample is chosen with replacement, each individual has the same chance of selection on every draw. b. A sample is always a good representation of the target population. c. Items or individuals in a judgement sample are chosen with regard to their probability of occurrence. d. The lecturer of a business statistics class wanted to find out the average amount of time per week her students spent studying for the class. Among the 50 students in her class, 20% were first-year students, 50% were second-year students and 30% were third-year students. She decided to draw 2 students randomly from the first-year students, 5 randomly from the second-year students and 3 randomly from the third-year students. This is an example of a systematic sample. e. The lecturer of a business statistics class wanted to find out the average amount of time per week her students spent studying for the class. She divided the fifty students on her class list into ten groups starting from the first student on the roster. The first student was randomly selected from the first group. Then every tenth student was selected from the remaining students. This is an example of a cluster sample. 4. The height of an adult male is known to be normally distributed with a mean of 69 inches and a standard deviation of 2.5 inches. a. What is the probability that a randomly selected adult male has a height between 65 inches and 73 inches? b. What is the probability that a randomly selected adult male is either shorter than 64 inches or taller than 74 inches? c. What is the probability that a randomly selected adult male has a height between 70 inches and 72 inches? d. What is the height of the doorway such that 96 percent of the adult males can pass through it without having to duck their head? 5. Calculate Laspeyres Price Indexes for 2000-2002 from the following data. Use 1995 as the base year. Price 21 2001 0.25 2.Calculate the following probabilities for the mean is 17 and standard deviation is 2 P( X 17) P( X 18) P( X 15) P(15. Event D: The number on the top is less than 4.9 1.5 X 19) P(15 X 16) P( X 14 or X 20) P( X 18) 7.11 13.84 0.15 2000 0.A die is tossed and five events are defined as follows: Event A: The number on the top is even. Event C and Event D are mutually exclusive.68 1. e.85 Price 27.71 1.75 0. Event A and Event B are collectively exhaustive.25 Calculate the Paasche Price Indexes for 2001 and 2002 using the following data and 1997 as the base year 2001 Item 1 2 3 Price(1997) 22.25 2002 0.75 0. T / T / T / T / T / F F F F F .9 0.25 Quantity 13 5 41 Price 28. Event C: The number on the top is greater than 4.91 0. Event C and Event D are collectively exhaustive.5 10.67 1.35 2002 Quantity 12 8 44 6.8 0.8 13.85 0. b. Event B: The number on the top is odd. Event A and Event B are mutually exclusive. Event E: The number on the top is more than 2 Determine whether the following statements are true: a. d. Event E and Event D are collectively exhaustive.Item 1 2 3 4 Quantity (1995) 21 6 17 43 1995 0. c.1 2.23 0.5 1. and.The quality management officer of a financial services firm is concerned with the number of customers who are complaining about the service charges they are paying when they take out a loan. a. 312 of the 937 men had at least one parent who suffered from heart disease. find the upper and lower readings that would qualify people to participate in the study. a researcher wishes to select people in the middle 60% of the population based on blood pressure. 11. Moreover. Determine the probability that a man randomly sepected from this group died of causes related to heart disease. If we draw the probability graph of this 20 trials.1. Assume that blood pressure readings are normally distributed. What is the probability that number of complaining customers will be less than the average? d.30 0. x –$1000 $0 +$1000 +$2000 +$4000 Totals: P(x) 0.f. it will look …………… skewed because …………. If the mean systolic blood pressure is 120 and standard deviation 8. Surveys of bank customers have found that the probability a customer is unhappy about the charges is p = 0. Event E and Event D are mutually exclusive. 12. What is the average number of customers who are unhappy about the changes? b.10 The mean and standard deviation of this distribution are ___________and ___________.A public heath researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of these men died from causes related to health disease. of these 312 men.20 0. 9. she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product. T / F 8. What is the standard deviation? c. Based on her 15 years experience. This is an example of assigning probabilities by the ________________ method. given that neither of his parents suffered from heart disease.20 0.Belinda Boyd is reviewing a newly proposed advertising campaign.You are offered an investment opportunity.For a medical study. As these people have been interviewed independently of each other we can assume that the number who complain has a Binomial distribution. Its outcomes and probabilities are presented in the following table. A sample of n = 20 people are interviewed and asked whether they are unhappy about these charges.. 10. 102 died from causes related to heart disease. .20 0. 000 gallons of milk. f. d.40 .10 0. what is the probability that this student is enrolled neither in Statistics nor in Accounting? 14. Because of variation in the market price of milk and cost of feeding the cows. Estimate the profit on the 25. Investment Objective Growth Income Total Electronics 100 20 120 Industry Sector Airlines 10 20 30 Healthcare 40 10 50 Total 150 50 200 a.04 -$0. P(Growth) = _______. P(Growth Income) = _______.Let A be the event that a student is enrolled in an accounting course. P(Healthcare) = _______.38 $0.A dairy farmer estimates for the next year the farm‟s cows will produce about 25. If a stock is selected randomly from Meagan‟s portfolio.Meagan Davies manages a portfolio of 200 common stocks. P(Healthcare Electronics) = ______.000 gallons.A used-car dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased. It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics. e.32 . and let S be the event that a student is enrolled in a statistics course.00 Buyer Female Gender Male Total Are „Female‟ and „4WD‟ independent. If a stock is selected randomly from Meagan‟s portfolio. A student is randomly selected.30 $0. 13. If a stock is selected randomly from Meagan‟s portfolio. c. P(Growth | Healthcare) = _____.02 . the profit per gallon may vary with the probabilities given in the table below. Gain per gallon Probability $1. Her staff classified the portfolio stocks by „industry sector‟ and „investment objective‟.90 0.00 0.48 1.06 $0.12. If a stock is selected randomly from Meagan‟s portfolio. P(Airlines | Income) = _______. The following joint probability table was developed from the dealer‟s records for the previous year. Type of Vehicle 4WD Not 4WD Total . b. why or why not? 15. Included in these numbers are 15% who are enrolled in both statistics and accounting.40 0. If a stock is selected randomly from Meagan‟s portfolio.20 $0.70 0.10 0. If a stock is selected randomly from Meagan‟s portfolio. a. 20% of all plant employees are absent excessively. What is the probability that mean of randomly selected 9 students’ grades is higher than 85? c. What is the standard deviation of home insurance costs in Vietnam? 21. Calculate the probability that insurance cost of a randomly selected home is between $450 and $680? e. d.Suppose home insurance costs in Vietnam are uniformly distributed with the range of from $100 to $900. What is the probability that a randomly selected student got a grade higher than 85? b. If 40% of the names on the list are not authentic. a. Are the answers from a and b different? Why so? Explain in your own words d. f. is exploring employee absenteeism at Plain Power Plant. P(x<2) is ______________.16. What is your expected gain if you buy the contract? 17. P(A F) =………….The quality control manager at a light bulb factory needs to estimate the proportion of defective light bulbs in a shipment of 1. Ten per cent of all plant employees work in the finishing department. a.Lucy Liu purchased a mailing list of 2000 names and addresses for her mail order business. and A is the event „is absent excessively‟. and 7% of all plant employees work in the finishing department and are absent excessively. She randomly selects five names from the list for validation.A set of final examination grades in an introductory statistics course was found to be normally distributed with a mean of 73 and a standard deviation of 10. Create an interval such that 95% of all possible sample proportions of defective . If you buy the contract. but after scanning the list she doubts the authenticity of the list. Consumer information shows that 12% of the televisions like yours require an annual repair that costs $140 on the average. F is the event „works in the finishing department‟. Find the interval of middle 90% for the mean of randomly selected sample of 16 students. Calculate the probability that insurance cost of a randomly selected home is less than $300? d. and x is the number of non-authentic names in her sample. 18.Adam Shapiro.000 bulbs. Director of Human Resources. Find the first and third quartiles for the population e. all repairs for one year are free. It is known that 5% of light bulbs manufactured by the factory is defective. Draw the graph of the distribution and plot the values on it. What is the probability density function (pdf) for the distribution? c. Is the population size large enough in relation to the sample size that we can ignore the finite population correction factor in our calculation of the Standard Error of the sample proportion of defective bulbs? b. A plant employee is selected randomly. If the teacher decides only the lowest 15% of the students will fail. Verify that the sample size is large enough to justify applying the Central Limit Theorem. what is the grade whose below fails? 20. b.Suppose the warranty period on your family’s new television is about to expire and you are debating about whether to buy a one-year maintenance contract for $35. Calculate the expected value and the Standard Error of the sample proportion of defective bulbs. What is the mean cost of home insurance in Vietnam? f. 19. c. What is the probability that the number of defective bulbs in the sample is between 45 and 55? f.bulbs will be within e. Suppose that the customer decides to return the entire shipment if the defective bulb rate exceeds 7%. What is the probability that the shipment will not return? .