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 2 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

CRA CDs Inc. wants the mean lengths of the “cuts” on a CD to be 135 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? 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?

The mean amount purchased by a typical customer at Churchill’s Grocery Store is $23.50, with a standard deviation of$5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions. a. What is the likelihood the sample mean is at least $25.00? b. What is the likelihood the sample mean is greater than$22.50 but less than $25.00? c. Within what limits will 90 percent of the sample means occur?

Majesty Video Production Inc. wants the mean length of its advertisements to be 30 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 16 ads produced by Majesty.

a. What can we say about the shape of the distribution of the sample mean time?

b. What is the standard error of the mean time?

c. What percent of the sample means will be greater than 3 1.25 seconds?

d. What percent of the sample means will be greater than 28.25 seconds?

e . What percent of the sample means will be greater than 28.25 but less than 3 1.25 seconds?

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 b. The sample of 10 could have been chosen using a systematic sample. Choose the first number, 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?

Sid went to his attorney’s office and described in detail how he wanted his estate distributed upon his death. The lawyer made extensive notes and prepared a 12-page will. He called Sid and read it to him over the phone. Sid made a few minor changes. The lawyer then prepared a final copy. On his way to the lawyer’s office to sign the document, Sid died of a heart attack. Was the final copy a valid will? Why or why not?

On February 1, the Miro Company needs to purchase some office equipment. The company is short of cash and expects to be short for several months. The treasurer has said that he could pay for the equipment as follows.

$$\begin{matrix} \text{Date} & \text{Payment}\\ \text{April. 1} & \text{\$150}\\ \text{June. 1} & \text{300}\\ \text{Aug. 1} & \text{450}\\ \text{Oct. 1} & \text{600}\\ \text{Dec. 1} & \text{750}\\ \end{matrix}$$

A local office supply firm will agree to sell the equipment to Miro now and accept payment according to the treasurer's schedule. If interest will be charged at 3% every 2 months, with compounding once every 2 months, how much office equipment can the Miro Company buy now? What is the effective interest rate?

A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Compute the probability the sample mean is: a. Less than 74. b. Between 74 and 76. c. Between 76 and 77. d. Greater than 77

Suppose your statistics instructor gave six examinations during the semester. You received the following grades: 79, 64, 84, 82, 92, and 77. Instead of averaging the six scores, the instructor indicated he would randomly select two grades and compute the final percent correct based on the two percents. a. How many different samples of two test grades are possible? b. List all possible samples of size two and compute the mean of each. c. Compute the mean of the sample means and compare it to the population mean. d. If you were a student, would you like this arrangement? Would the result be different from dropping the lowest score? Write a brief report.

The manufacturer of eMachines, an economy-priced computer, recently completed the design for a new laptop model. eMachine’s top management would like some assistance in pricing the new laptop. Two market research firms were contacted and asked to prepare a pricing strategy. Marketing-Gets-Results tested the new eMachines laptop with 50 randomly selected consumers, who indicated they plan to purchase a laptop within the next year. The second marketing research firm, called MarketingReaps-Profits, test-marketed the new eMachines laptop with 200 current laptop owners. Which of the marketing research companies’ test results will be more useful? Discuss why.

The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.8 years. The standard deviation of the distribution is 2.5 years. For a random sample of 60 men, what is the likelihood that the age at which they were married for the first time is less than 25.1 years?

A population consists of the following five values: 2, 2, 4, 4, and 8. a. List all samples of size 2, and compute the mean of each sample. b. Compute the mean of the distribution of sample means and the population mean. Compare the two values. c. Compare the dispersion in the population with that of the sample means

Five sales representatives work for Mid-Motors Ford. The five associates' sales of automobiles during the previous week are as follows:

$$\begin{array}{|lc|} \hline \text { Sales Associate } & \text { Cars Sold } \\ \hline \text { Peter Hankish } & 8 \\ \text { Connie Stallter } & 6 \\ \text { Juan Lopez } & 4 \\ \text { Ted Barnes } & 10 \\ \text { Peggy Chu } & 6 \\ \hline \end{array}$$

Compare the mean of the sampling distribution of the sample mean with that of the population.

A population consists of the following four values: 12, 12, 14, and 16. a. List all samples of size 2, and compute the mean of each sample. b. Compute the mean of the distribution of the sample mean and the population mean. Compare the two values. c. Compare the dispersion in the population with that of the sample mean