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| m223 | 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 inter-viewed 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.4.
b. The sample of 10 could have been chosen using a systematic sample. Choose the first number using Appendix B.4, 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? |
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| m224 | As part of a recent survey among dual-wage-earner couples, an industrial psychologist found that 990 men out of the 1,500 surveyed believed the division of household duties was fair. A sample of 1,600 women found 970 believed the division of household duties was fair. At the .01 significance level, is it reasonable to conclude that the proportion of men who believe the division of household duties is fair is larger? What is the p-value? |
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| m225 | As part of a study of corporate employees, the director of human resources for PNC Inc. wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month. The population standard deviations for the Cincinnati and Pittsburgh employees are 30 and 26 miles, respectively. At the .05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees? |
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| m226 | An assembly consists of three mechanical components. Suppose that the probabilities that the first, second, and third components meet specifications are 0.95, 0.98, and 0.99. Assume that the components are independent. Determine the probability mass function of the number of components in the assembly that meet specifications. |
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| m228 | Assembly workers at Coastal Computers Inc. assemble just one or two subassemblies and insert them in a frame. The executives at CC think that the employees would have more pride in their work if they assembled all of the subassemblies and tested the complete computer. A sample of 25 employees was selected to experiment with the idea. After a training program, each was asked his or her preference. Twenty liked assembling the entire unit and testing it. At the .05 level, can we conclude the employees preferred assembling the entire unit? Explain the steps you used to arrive at your decision. |
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| m229 | Assume a binomial distribution where n 5 3 and p 5 .60.
a. Refer to Appendix B.1, and list the probabilities for values of x from 0 to 3.
b. Determine the mean and standard deviation of the distribution from the general definitions given in formulas (6–1) and (6–2). |
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| m230 | Assume a binomial distribution where n 5 5 and p 5 .30.
a. Refer to Appendix B.1 and list the probabilities for values of x from 0 to 5.
b. Determine the mean and standard deviation of the distribution from the general definitions given in formulas (6–1) and (6–2). |
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| m231 | Assume a binomial probability distribution with n 5 40 and p 5 .55. Compute the following:
a. The mean and standard deviation of the random variable.
b. The probability that x is 25 or greater.
c. The probability that x is 15 or less.
d. The probability that x is between 15 and 25, inclusive. |
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| m232 | Assume a binomial probability distribution with n 5 50 and p 5 .25. Compute the following:
a. The mean and standard deviation of the random variable.
b. The probability that x is 15 or more.
c. The probability that x is 10 or less. |
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| m233 | Assume that each of your calls to a popular radio station has a probability of 0.02 of connecting, that is, of not obtaining a busy signal. Assume that your calls are independent.
(a) What is the probability that your first call that connects is your tenth call?
(b) What is the probability that it requires more than five calls for you to connect?
(c) What is the mean number of calls needed to connect? |
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| m234 | Assume the likelihood that any flight on Delta Airlines arrives within 15 minutes of the scheduled time is .90. We randomly selected a Delta flight on four different days.
a. What is the likelihood all four of the selected flights arrived within 15 minutes of the scheduled time?
b. What is the likelihood that none of the selected flights arrived within 15 minutes of the scheduled time?
c. What is the likelihood at least one of the selected flights did not arrive within 15 minutes of the scheduled time? |
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| m235 | Assume the number of errors along a magnetic recording surface is a Poisson random variable with a mean of one error every 105 bits. A sector of data consists of 4096 eight-bit bytes. (a) What is the probability of more than one error in a sector? (b) What is the mean number of sectors until an error is found? |
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| m236 | At Rumsey’s Old Fashion Roast Beef, cola drinks are filled by an automatic machine whose operation is based on the weight of the drink. When the process is in control, the machine fills each cup so that the grand mean is 10.0 ounces and the mean range is 0.25 for samples of 5.
a. Determine the upper and lower control limits for the process for both the mean and the range.
b. The manager of the I-280 store tested five soft drinks served last hour and found that the mean was 10.16 ounces and the range was 0.35 ounce. Is the process in control? Should other action be taken? |
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| m237 | At the beginning of each football season, Team Sports, the local sporting goods store, purchases 5,000 footballs. A sample of 25 balls is selected, and they are inflated, tested, and then deflated. If more than two balls are found defective, the lot of 5,000 is returned to the manufacturer. Develop an OC curve for this sampling plan.
a. What are the probabilities of accepting lots that are 10%, 20%, and 30% defective?
b. Estimate the probability of accepting a lot that is 15% defective.
c. John Brennen, owner of Team Sports, would like the probability of accepting a lot that is 5% defective to be more than 90%. Does this appear to be the case with this sampling plan? |
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| m238 | At the downtown office of First National Bank, there are five tellers. Last week, the tellers made the following number of errors each: 2, 3, 5, 3, and 5.
a. How many different samples of two tellers are possible?
b. List all possible samples of size 2 and compute the mean of each.
c. Compute the mean of the sample means and compare it to the population mean. |
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| m239 | At the January national sales meeting, the CEO of Kimble Products was questioned extensively regarding the company policy for paying commissions to its sales representatives. The company sells sporting goods to two major markets. There are 40 sales representatives who call directly on large-volume customers, such as the athletic departments at major colleges and universities and professional sports franchises. There are 30 sales representatives who represent the company to retail stores located in shopping malls and large discounters such as Kmart and Target.
Upon his return to corporate headquarters, the CEO asked the sales manager for a report comparing the commissions earned last year by the two parts of the sales team. The information is reported below. Write a brief report. Would you conclude that there is a difference? Be sure to include information in the report on both the central tendency and dispersion of the twogroups. |
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| m240 | At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $80 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $9.95. Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $84.85. At the .01 significance level, can Ms. Brigden conclude that her daily tips average more than $80?
(a) State the null hypothesis and the alternate hypothesis.
(b) State the decision rule.
(c) Compute the value of the test statistic.
(d) What is your decision regarding H0?
(e) What is the p-value? Interpret it. |
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| m241 | Automatic Screen Door Manufacturing Company purchases door latches from a number of vendors. The purchasing department is responsible for inspecting the incoming latches. Automatic purchases 10,000 door latches per month and inspects 20 latches selected at random. Develop an OC curve for the sampling plan if three latches can be defective and the incoming lot is still accepted. |
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| m242 | Automobiles arrive at the Elkhart exit of the Indiana Toll Road at the rate of two per minute. The distribution of arrivals approximates a Poisson distribution.
a. What is the probability that no automobiles arrive in a particular minute?
b. What is the probability that at least one automobile arrives during a particular minute? |
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| m243 | Bank of America customers select their own three-digit personal identification number
(PIN) for use at ATMs.
a. Think of this as an experiment and list four possible outcomes.
b. What is the probability Mr. Jones and Mrs. Smith select the same PIN?
c. Which concept of probability did you use to answer (b)? |
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