Suppose the average number of returns processed by employees of a tax preparation service during tax season is 12 per day with a standard deviation of 5 per day. A random sample of 36 employees taken during tax season revealed the number of returns processed daily shown below. Use these data to answer parts a through c.

17

9

16

10

8

16

14

15

9

14

15

15

11

13

15

12

13

15

8

10

8

16

15

11

10

8

17

12

13

13

5

5

23

9

9

21

a. What is the probability of having a sample mean equal to or smaller than the sample mean for this sample if the population mean is 12 processed returns daily with a standard deviation of 5 returns perday?

b. What is the probability of having a sample mean larger than the sample mean for this sample if the population mean is 12 processed returns daily with a standard deviation of 5 returns perday?

c. Explain how it is possible to answer parts a and b when the population distribution of daily tax returns at the tax firm is not known. Choose the correct answer below.

A.

All data are normally distributed.Thus, the distribution of the sample means will be approximately normal.

B.

The Central Limit Theorem can be applied because the sample size is sufficiently large.Thus, the distribution of the sample means will be approximately normal.

C.

The Central Limit Theorem can be applied because the sample size is sufficiently large.Thus, the distribution of the sample means will be either skewed to the left or skewed to the right.

D.

The Central Limit Theorem can be applied because the sample size is not large.Thus, the distribution of the sample means will be approximately normal.