Use the standard normal distribution or thet-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can beused, explain why. Interpret the results.

In a random sample of 20 mortgageinstitutions, the mean interest rate was 3.67% and the standard deviation was 0.35%. Assume the interest rates are normally distributed.

Which distribution should be used to construct the confidenceinterval?

A.

Use a normal distribution because the interest rates are normally distributed and is known.

B.

Use at-distribution because it is a randomsample, isunknown, and the interest rates are normally distributed.

C.

Use a normal distribution because n<30 and the interest rates are normally distributed.

D.

Use at-distribution because the interest rates are normally distributed and is known.

E.

Cannot use the standard normal distribution or thet-distribution because isunknown, n<30, and the interest rates are not normally distributed.

Select the correct choice belowand, ifnecessary, fill in any answer boxes to complete your choice.

A.

The 95% confidence interval is (

nothing

,

nothing

).

(Round to two decimal places asneeded.)

B.

Neither distribution can be used to construct the confidence interval.

Interpret the results. Choose the correct answer below.

A.

With 95% confidence, it can be said that the population mean interest rate is between the bounds of the confidence interval.

B.

It can be said that 95% of institutions have an interest rate between the bounds of the confidence interval.

C.

If a large sample of institutions are taken approximately 95% of them will have an interest rate between the bounds of the confidence interval.

D.

Neither distribution can be used to construct the confidence interval.