The mean height for the population probability distribution of heights is 65 inches and the standard deviation is 3 inches.
A) Is it stated that the distribution of heights is a normal distribution?
B) If a random sample of 16 people is obtained from the above population, can the sampling distribution of sample means be assumed to have a normal distribution? Why or why not.
C) If a random sample of 36 people is obtained from the above population, can the sampling distribution of sample means be assumed to have a normal distribution? Why or why not.
D) IF the answer in part C is yes, find the probability that the mean height of a random sample of 36 people is within 1 inch of the population mean.