A variable of a population has a mean of

=78

and a standard deviation of

=24.

a. Identify the sampling distribution of the sample mean for samples of size

36.

b. In answering part (a), what assumptions did you make about the distribution of the variable?

c. Can you answer part (a) if the sample size is

25

instead of

36?

Why or why not?

a. What is the shape of the sampling distribution?

normal

uniform

skewed

bimodal

What is the mean of the sampling distribution?

x=enter your response here

(Simplify your answer.)

What is the standard deviation of the sampling distribution?

x=enter your response here

(Simplify your answer.)

b. In answering part (a), what assumptions did you make about the distribution of the variable?

A.

It was assumed that the distribution of the variable was unimodal.

B.

It was assumed that the variable was normally distributed.

C.

No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideration.

D.

No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration.

c. Can you answer part (a) if the sample size is

25

instead of

36?

Why or why not?

A.

No, because the sample size must be less than 5 if the distribution of the variable is unknown.

B.

Yes, because the sample size must be less than 30 if the distribution of the variable is unknown.

C.

No, because the sample size needs to be at least 30 if the distribution of the variable is unknown.

D.

Yes, because the sample size makes no difference in determining the sampling distribution.