Average weight gain for a sample of 25 patients who took the experimental anti-anxiety drug Ferin in a controlled six-month experiment was 21.4 lbs.,...

Average weight gain for a sample of 25 patients who took the experimental anti-anxiety drug Ferin in a controlled six-month experiment was 21.4 lbs., with a sample standard deviation of 5.1 lbs. Assume the population distribution of weight gain for all patients who take Ferin is normal. 

a. Build a 99% confidence interval estimate of the average weight gain for the population of all patients represented by the sample (that is, the population of all patients who take this drug). 

b. Show the 99% confidence interval if the size of the sample was 12.