Suppose that the weekly average expenditure of a student in your college is $150 with a variance of $81. (a) Suppose you draw a sample of 100 students. Compute the probability that the sample mean is less than $147. (b) Suppose now that you draw a sample of 36 students. Compute the probability that the sample mean is less that $147. Why is this result different from that in part (a)? (c) With a sample of 64 students, compute the probability that the sample mean falls between $149 and $151.