The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,200 per month and a standard deviation of$250 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 50 one bedroom apartments and finding the mean to be at least $1,950 per month?

Nike’s annual report says that the average American buys 6.5 pairs of sports shoes per year. Suppose the population standard deviation is 2.1 and that a sample of 81 customers will be examined next year. a. What is the standard error of the mean in this experiment? b. What is the probability that the sample mean is between 6 and 7 pairs of sports shoes? c. What is the probability that the difference between the sample mean and the population mean is less than 0.25 pairs? d. What is the likelihood the sample mean is greater than 7 pairs?

According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers. a. What is the standard error of the mean in this example? b. What is the likelihood the sample mean is greater than 320 minutes? c. What is the likelihood the sample mean is between 320 and 350 minutes? d. What is the likelihood the sample mean is greater than 350 minutes?

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?

Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,000 pounds and the standard deviation is 150 pounds. Assume that the population follows the normal distribution. Forty trucks are randomly selected and weighed. Within what limits will 95 percent of the sample means occur?

Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. 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 $112,000? 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$112,000

There are five sales associates at Mid-Motors Ford. The five associates and the number of cars they sold last week are:

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

a. How many different samples of size 2 are possible? b. List all possible samples of size 2 , and compute the mean of each sample. c. Compare the mean of the sampling distribution of the sample mean with that of the population. d. On a chart similar to Chart $8-2$, compare the dispersion in sample means with that of the population.

The mean in a normal population is 60, and the standard deviation is 12. You choose nine at random. Calculate the probability that the sample mean is between 56 and 63

A sample of 250 observations is selected from a normal population for which the population standard deviation is known to be 25. The sample mean is 20. a. Determine the standard error of the mean. b. Explain why we can use formula to determine the 95 percent confidence interval. c. Determine the 95 percent confidence interval for the population mean

Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be the population values.

$$\begin{array}{llllllllllllllllllll} 2 & 3 & 2 & 3 & 3 & 4 & 2 & 4 & 3 & 2 & 2 & 7 & 3 & 4 & 5 & 3 & 3 & 3 & 3 & 5 \end{array}$$

a. Draw a graph showing the population distribution. b. Compute the mean of the population. c. Select five random samples of five each. Compute the mean of each sample. Use the methods described in this chapter. Using a random number table (Appendix B.4) or statistical software, select the items to be included in the sample. d. Compare the mean of the sampling distribution of the sample mean to the population mean. Would you expect the two values to be about the same? e. Draw a histogram of the sample means. Why are the two distributions different?

Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,100 per hour and a standard deviation of$250. What is the operating cost for the lowest 3 percent of the airplanes?

The mean SAT score for Division I student-athletes is 947 with a standard deviation of 205. If you select a random sample of 60 of these students, what is the probability the mean is below 900?

According to all student records at Camford University, students participate in organised sports 5.5 hours per week on average. The weekly standard deviation for the population is 2.2 hours. Healthy Lifestyles Incorporated (HLI) wants to use the central limit theorem to make a number of estimates based on a sample of 121 pupils. Using this Compute the standard error of the sample mean.

Sam Snead's restaurant in Conway, South Carolina, offers an early bird special from 4-6 pm each week day evening. If each patron selects a Starter Selection (4 options), an Entree (8 options), and a Dessert (3 options), how many different meals are possible?