A simple random sample of size n is drawn from a population that is normally distributed. The samplemean, x, is found to be 111, and the sample standarddeviation, s, is found to be 10.

(a) Construct a 95% confidence interval about if the samplesize, n, is 13.

(b) Construct a 95% confidence interval about if the samplesize, n, is 20.

(c) Construct a 96% confidence interval about if the samplesize, n, is 13.

(d) Could we have computed the confidence intervals in parts(a)-(c) if the population had not been normallydistributed?

(a) Construct a 95% confidence interval about if the samplesize, n, is 13.

Lowerbound:

; Upperbound:

(Use ascending order. Round to one decimal place asneeded.)

(b) Construct a 95% confidence interval about if the samplesize, n, is 20.

Lowerbound:

; Upperbound:

(Use ascending order. Round to one decimal place asneeded.)

How does increasing the sample size affect the margin oferror, E?

A.

As the sample size increases, the margin of error increases.

B.

As the sample size increases, the margin of error decreases.

C.

As the sample size increases, the margin of error stays the same.

(c) Construct a 96% confidence interval about if the samplesize, n, is 13.

Lowerbound:

; Upperbound:

(Use ascending order. Round to one decimal place asneeded.)

Compare the results to those obtained in part(a). How does increasing the level of confidence affect the size of the margin oferror, E?

A.

As the level of confidence increases, the size of the interval stays the same.

B.

As the level of confidence increases, the size of the interval increases.

C.

As the level of confidence increases, the size of the interval decreases.

(d) Could we have computed the confidence intervals in parts(a)-(c) if the population had not been normallydistributed?

A.

No, the population needs to be normally distributed.

B.

Yes, the population needs to be normally distributed.

C.

Yes, the population does not need to be normally distributed.

D.

No, the population does not need to be normally distributed.

please show work