Data on salaries in the public school system are published annually by a teachers' association. The mean annual salary of (public) classroom teachers is

$55.4

thousand. Assume a standard deviation of

$8.0

thousand. Complete parts (a) through (e) below.

Question content area bottom

Part 1

a. Determine the sampling distribution of the sample mean for samples of size 64.

The mean of the sample mean is

x=$enter your response here.

(Type an integer or a decimal. Do not round.)

Part 2

The standard deviation of the sample mean is

x=$enter your response here.

(Type an integer or a decimal. Do not round.)

Part 3

b. Determine the sampling distribution of the sample mean for samples of size 256.

The mean of the sample mean is

x=$enter your response here.

(Type an integer or a decimal. Do not round.)

Part 4

The standard deviation of the sample mean is

x=$enter your response here.

(Type an integer or a decimal. Do not round.)

Part 5

c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.

A.

Yes, because

x

is only normally distributed if x is normally distributed.

B.

No, because if

x

is normally distributed, then x must be normally distributed.

C.

No, because the sample sizes are sufficiently large so that

x

will be approximately normally distributed, regardless of the distribution of x.

D.

Yes, because the sample sizes are not sufficiently large so that

x

will be approximately normally distributed, regardless of the distribution of x.

Part 6

d. What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most $1000?

enter your response here

(Round to three decimal places as needed.)

Part 7

e. What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 256 classroom teachers will be at most $1000?

enter your response here

(Round to three decimal places as needed.)