A pediatrician has found that the heights of their patients follow a normal distribution with mean = 40 inches and standard deviation = 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 ofor SRSs of size 12.

(b) Find the probability that the mean height is greater than 48.2 inches.