21. A statistics student wishes to determine the mean height of US males who are 20 or older. Assume height is normally distributed. He takes a sample of 19 US males who are 20 or older. The mean was 71.2 inches and the standard deviation was 3.05 inches.

a. Show that the Central Limit Theorem of Means applies to the sampling distribution of means of samples of 19 US males who are 20 or older. Provide proof.

b. Describe the sampling distribution of means of samples of 19 US males who are 20 or older.

c. make a 96% confidence interval estimate for the mean height of all US males who are 20 or. Round to two decimal places and Interpret

e. What size sample is necessary to reduce the maximum error to 0.5 inch?