d) The sales manager wants to award the sales representatives who earn the commissions a bonus of $ He can award a bonus to 20 percent of the

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1 NORTON UNIVERSITY Department of Business Group: Bu2M1, M2, M5, M6 Semester 2, Academic Year ASSIGNMENT Course Title: Business and Economics Statistics Lecturer: Mr. MONG Mara Deadline: June 14, ) The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. a) Determine the z values for 29 and 34 hours. What percent of the garages take between32 hours and 34 hours to erect? b) What percent of the garages take between 29 hours and 34 hours to erect? c) What percent of the garages take 28.7 hours or less to erect? d) Of the garages, 5 percent take how many hours or more to erect? 2) A study of long-distance phone calls made from the corporate offices of Pepsi Bottling Group, Inc., in Somers, New York, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes. a) What fraction of the calls last between 4.2 and 5 minutes? b) What fraction of the calls last more than 5 minutes? c) What fraction of the calls last between 5 and 6 minutes? d) What fraction of the calls last between 4 and 6 minutes? e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4 percent of the calls. What is this time? 3) The annual commissions earned by sates representatives of Machine Products, Inc., a manufacturer of light machinery, follow the normal probability distribution. The mean yearly amount earned is $40,000 and the standard deviation is $5,000. a) What percent of the sates representatives earn more than 42,000 per year? b) What percent of the sales representatives earn between $32,000 and $42.000? c) What percent of the sales representatives earn between $32,000 and $35,0007 1

2 d) The sales manager wants to award the sales representatives who earn the commissions a bonus of $ He can award a bonus to 20 percent of the representatives. What is the cutoff point between those who earn a bonus and those who do not? 4) According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,994. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $450. a) What percent of the adults spend more than $2,500 per year on reading and entertainment? b) What percent spend between $2,500 and $3.000 per year on reading and entertainment? c) What percent spend less than 31,000 per year on reading and entertainment? 5) Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles. a) What percent of the Ford Super Duty F-7503 tagged 65,200 miles or more? b) What percent of the trucks logged more than 57,060 but less than 58,280 miles? c) What percent of the Fords traveled 62,000 miles or less during the year? d) Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles? 6) A recent report in BusinessWeek indicated that 20 percent of all employees steal from their company each year. If a company employs 50 people, what is the probability that: a) Fewer than 5 employees steal? b) More than 5 employees steal? c) Exactly 5 employees steal? d) More than 5 but fewer than 15 employees steal? 7) It is estimated that 10 percent of those taking the quantitative methods portion of the CPA examination fail that section. Sixty students are taking the exam this Saturday. a) How many would you expect to fail? What is the standard deviation? b) What is the probability that exactly two students will fail? c) What is the probability at least two students will fail? 8) Cruise ships of the Royal Viking line report that 60 percent of their rooms are occupied during September. For a cruise ship having 800 rooms, what is the probability that 665 or more are occupied in September? 9) In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.5 hours per week playing organized sports. The population's standard deviation is 2.2 hours per week. Based on a sample of 121 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates. a) Compute the standard error of the sample mean. 2

3 b) What is the chance HLI will find a sample mean between 5 and 6 hours? c) Calculate the probability that the sample mean will be between 5.3 and 5.7 hours. d) How strange would it be to obtain a sample mean greater than 6.5 hours? 10) Answer the following questions in one or two well-constructed sentences. a) What happens to the standard error of the mean if the sample size is increased? b) What happens to the distribution of the sample means if the sample size in increased? c) When using the distribution of sample means to estimate the population mean, what is the benefit of using larger sample sizes? 11) As a part of their customer-service program, United Airlines randomly selected 10 passengers from today's 9 A.M. Chicago-Tampa flight. Each sampled passenger is to be interviewed in depth regarding airport facilities, service, and so on. To identify the sample, each passenger was given a number on boarding the aircraft. The numbers started with 001 and ended with 250. a) Select 10 usable numbers at random using Appendix B.6. b) The sample of 10 could have been chosen using a systematic sample. Choose the first number using Appendix B.6, and then list the numbers to be interviewed. c) Evaluate the two methods by giving the advantages and possible disadvantages. d) In what other way could a random sample be selected from the 250 passengers? 12) The appliance center has six sales representatives at its North Jacksonville outlet. Listed below is the number of refrigerators sold by each last month. Sales Number Sales Number Representatives Sold Representatives Sold Zina Craft 64 Jan 48 Woon Junge 50 Molly 50 Erie Debrul 52 Machel Myak 52 a) How many samples of size 2 are possible? b) Select all possible samples of size 2 and compute the mean number sold. c) Organize the sample means into a frequency distribution. d) What is the mean of the population? What is the mean of the sample means? e) What is the shape of the population distribution? f) What is the shape of the distribution of the sample mean? 13) CRA CDs, Inc., wants the mean lengths of the "cuts" on a CD to be 135 seconds (2 minutes and 15 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with a population standard deviation of 8 seconds. Suppose we select a sample of 16 cuts from various CDs sold by CRA CDs, Inc. a) What can we say about the shape of the distribution of the sample mean? b) What is the standard error of the mean? c) What percent of the sample means will be greater than 140 seconds? 3

4 d) What percent of the sample means will be greater than 128 seconds? e) What percent of the sample means will be greater than 128 but less than 140 seconds? 14) Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $ This distribution follows the normal distribution with a standard deviation of $40,000, a) If we select a random sample of 50 households, what is the standard error of the mean? b) What is the expected shape of the distribution of the sample mean? c) What is the likelihood of selecting a sample with a mean of at least $112,0007 d) What is the likelihood of selecting a sample with a mean of more than $100,000? e) Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112, ) A random sample of 85 group leaders, supervisors, and similar personnel at General Motors revealed that, on the average, they spent 6.5 years on the job before being promoted; the standard deviation of the sample was 1.7 years. Construct a 95 percent confidence interval. 16) A state meat inspector in lows has been given the assignment of estimating the mean net weight of packages of ground chuck labeled "3 pounds." Of course, he realizes that the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean weight to be 3.01 pounds, with a standard deviation of 0.03 pounds. a) What is the estimated population mean? b) Determine a 95 percent confidence interval for the population mean. 17) A recent survey of 50 executives who were laid off from their previous position revealed it took a mean of 26 weeks for them to find another position. The standard deviation of the sample was 6.2 weeks. Construct a 95 percent confidence interval for the population mean. Is it reasonable that the population mean is 28 weeks? Justify your answer. 18) The American Restaurant Association collected information on the number of meals eaten outside the home per week by young married couples. A survey of 60 couples showed the sample mean number of meals eaten outside the home was 276 meals per week, with a standard deviation of 0.75 meals per week. Construct a 97 percent confidence interval for the population mean. 19) In a poll to estimate presidential popularity, each person in a random sample of 1,000 voters was asked to agree with one of the following statements: 1. The president is doing a good job. 2. The president is doing a poor job. 3. I have no opinion. A total of 560 respondents selected the first statement, indicating they thought the president was doing a good job. 4

5 a) Construct a 95 percent confidence interval for the proportion of respondents who feel the president is doing a good job. b) Based on your interval in part (a), is it reasonable to conclude that a majority (more than half) of the population believes the president is doing a good job? 20) The First National Bank of Wilson has 650 checking account customers. A recent sample of 50 of these customers showed 26 to have a Visa card with the bank. Construct the 99 percent confidence interval for the proportion of checking account customers who have a Visa card with the bank. 21) You need to estimate the mean number of travel days per year for outside salespeople. The mean of a small pilot study was 150 days, with a standard deviation of 14 days. If you must estimate the population mean within 2 days, how many outside salespeople should you sample? Use the 90 percent confidence level. 22) Families USA, a monthly magazine that discusses issues related to health and health costs surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1, 000. a) Based on this sample information, develop a 90 percent confidence interval for the population mean yearly premium. b) How large a sample is needed to find the population mean within $250 at 99 percent confidence? 23) A random sample of 25 people employed by the Florida state authority established they earned an average wage (including benefits) of $65.00 per hour. The sample standard deviation was $6.25 per hour. a) What is the population mean? What is the best estimate of the population mean? b) Develop a 99 percent confidence interval for the population mean wage (including benefits) for these employees. c) How large a sample is needed to assess the population mean with an allowable error of $1.00" at 95 percent confidence? 24) According to the local union president, the mean gross income of plumbers in the Salt Lake area follows the normal probability distribution with a mean of $45,000 and a standard deviation of $3,000. A recent investigative reporter for KYAK TV found, for a sample of 120 plumbers, the mean gross income was $45,500. At the 0.10 significance level, is it reasonable to conclude that the mean income is not equal to $45,000? Determine the p-value. 25) Rutter Nursery Company packages its pine bark mulch in 50-pound bags. From a long history, the production department reports that the distribution of the bag weights follows the normal distribution and the standard deviation of this process is 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Below are the weights of 10 bags from today's production a) Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the.01 significance level. 5

6 b) In a brief report, tell why Mr. Butter can use the z distribution as the test statistic. c) Compute the p-value. 26) Dole Pineapple, Inc., is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is 0.03 ounces. The quality control department took a random sample of 50 cans and found that the arithmetic mean weight was ounces. At the 5 percent level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p-value. 27) According to a recent survey, Americans get a mean of 7 hours of sleep per night. A random sample of 50 students at West Virginia University revealed the mean number of hours slept last night was 6 hours and 48 minutes (6.8 hours). The standard deviation of the sample was 0.9 hours. Is it reasonable to conclude that students at West Virginia sleep less than the typical American? Compute the p-value. 28) A statewide real estate sales agency. Farm Associates, specializes in selling farm property in the state of Nebraska. Its records indicate that the mean selling time of farm property is 90 days. Because of recent drought conditions, the agency believes that the mean selling time is now greater than 90 days A statewide survey of 100 farms sold recently revealed that the mean selling time was 94 days, with a standard deviation of 22 days. At the 0.10 significance level, has there been an increase in selling time? 29) For a recent year the mean fare to fly from Charlotte, North Carolina, to Seattle, Washington, on a discount ticket was $267. A random sample of round-trip discount fares on this route last month gives: $321 $286 $290 $330 $310 $250 $270 $280 $299 $265 $291 $275 $281 At the 0.01 significance level can we conclude that the mean fare has increased? What is the p-value? 30) The publisher of Celebrity Living claims that the mean sales for personality magazines that feature people such as Angelina Jolie or Paris Hilton are 1.5 million copies per week. A sample of 10 comparable titles shows a mean weekly sales last week of 1.3 million copies with a standard deviation of 0.9 million copies. Does this data contradict the publisher's claim? Use the 0.01 significance level. 31) A United Nations report shows the mean family income for Mexican migrants to the United States is $27,000 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 25 Mexican family units reveals a mean to be $30,000 with a sample standard deviation of 310,000. Does this information disagree with the United Nations report? Apply the 0.01 significance level. 32) Traditionally, two percent of the citizens of the United States live in a foreign country because they are disenchanted with U.S. politics or social attitudes. In order to test if this proportion has increased since the September 11, 2001, terror attacks, U.S. consulates contacted a random sample of 400 of these expatriates. The sample yields 12 people who report they are living overseas because of political or social attitudes. Can you conclude this data shows the proportion of politically motivated expatriates has increased? Use the 0.05 significance level. 33) According to a study by the American Pet Food Dealers Association, 63 percent of U.S. households own pets. A report is being prepared for an 6

7 editorial in the San Francisco Chronicle. As a part of the editorial a random sample of 300 households showed 210 own pets. Does this data disagree with the Pet Food Dealers Association data? Use a 0.05 level of significance. Good Luck! 7