Question

In: Statistics and Probability

Suppose the average number of returns processed by employees of a tax preparation service during tax...

Suppose the average number of returns processed by employees of a tax preparation service during tax season is 10 per day with a standard deviation of 6 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.

14	14	13	13	9	13	13	11	16	13	17	13	14	11	13	13	14	14
10	10	7	17	13	10	10	17	7	8	11	10	6	4	13	9	9	5

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 10 processed returns daily with a standard deviation of 6 returns per day?The probability is (Round to four decimal places as needed.)

b. What is the probability of having a sample mean larger than the sample mean for this sample if the population mean is 10 processed returns daily with a standard deviation of 6 returns per day?The probability is (Round to four decimal places as needed.)

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. 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.

B. 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.

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

Expert Solution

Given:

Sample size, n = 36

Population standard deviation, = 6

Population mean, = 10

Therefore

a) The probability of having a sample mean equal to or smaller than the sample mean for this sample if the population mean is 10 processed returns daily with a standard deviation of 6 returns per day is 0.9332

b) The probability of having a sample mean larger than the sample mean for this sample if the population mean is 10 processed returns daily with a standard deviation of 6 returns per day is 0.0668

c) 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.

So A is the correct option.

orchestra answered 2 years ago

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