Business weekly conducted a survey of graduates for 30 top MBA programs. On the basis of the survey assume the means annual salary 10 years after graduation is $162,000. Assume the standard deviation...

Business weekly conducted a survey of graduates for 30 top MBA programs.  On the basis of the survey assume the means annual salary 10 years after graduation is $162,000.  Assume the standard deviation is $40,000.  Suppose you take a simply random sample of 39 graduates.  For a single randomly selected graduate, find the probability that her salary is between $156,692.00 and $161,395.00.

For a simple random sample of 39 graduates, find the probability that the average salary is between $156,692.00 and $161,395.00.  Is the assumption of normal necessary?  Yes, or No.