Statistics show on average an adult person receives 425 pieces of mail each year with a standard deviation of 50. What are the mean and the standard deviation of a sampling distribution if all possible samples of size 100 are selected?. What is the probability a person chosen at random received less than 475 pieces of mail in a year? What is the probability the mean of a random sample of 400 persons is more than 415 pieces of mail per year? Solution What are the mean and the standard deviation of a sampling distribution if all possible samples of size 100 are selected?. mean=425 standard deviation=50/n =50/10 =5.