A pediatrician has found that the heights of their patients follow a normal distribution with

mean p = 40 inches and standard deviation o = 10.2 inches. Each day the doctor sees 15

patients, which can be considered a representative sample of the doctor's patients. Each of

their heights is recorded and the mean is calculated.

(a) Calculate the mean and standard deviation of the sampling distribution of for SRSs of

size 15.

(b) Find the probability that the mean height is greater than 52.2 inches.