The following table gives the monthly salaries (in $1000s) of the six officers of a company.

a. Calculate the population mean monthly salary, μ. There are 15 possible samples of size 4 from the population of six officers. They are listed in the first column of the following table.

b. Complete the second and third columns of the table.
c. Complete the dotplot for the sampling distribution of the sample mean for samples of size 4. Locate the population mean on the graph.

d. Obtain the probability that the mean salary of a random sample of four officers will be within 1 (i.e., $1000) of the population mean.
e. Use the answer you obtained in part (b) and Definition 3.11 on page 128 to find the mean of the variable x-bar. Interpret your answer.
f. Can you obtain the mean of the variable x-bar without doing the calculation in part (e)? Explain your answer.

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Officer A B C D EF Salary 8 12 16 20 24 28 Sample A, B, C, D 8, 12, 16, 20 14 A, B, C, E 8, 12, 16, 24 5 A, B, C, F 8, 12, 16, 28 16 A, B, D, E 8, 12, 20, 24 16 A, B, D, F 8, 12, 20, 28 17 A, B, E, F 8, 12, 24, 28 18 A, C, D, E A, C, D, F A, C. E, F A, D, E, F B, C, D, E B, C, D, F B, C, E, F B, D, E, F C, D, E, F Xx 14 15 16 17 18 19 20 21 22