Use the standard normal distribution or thet-distribution to construct a

90% confidence interval for the population mean. Justify your decision. If neither distribution can beused, explain why. Interpret the results.

In a random sample of 12 mortgageinstitutions, the mean interest rate was 3.57% and the standard deviation was 0.36%. Assume the interest rates are normally distributed.

Which distribution should be used to construct the confidenceinterval?

A Use at-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.

Your answer is correct.

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

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

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 90% confidence interval is

(Round to two decimal places asneeded.)

B.Neither distribution can be used to construct the confidence interval