The Dean of Science at a large university claims that the starting salaries of its MSc graduates are normally distributed with a mean of $60,000 and a standard deviation of $4,000.
(a) Define the population random variable and state the information given about it. For (b), (c) and (d), define the random variable for each one and state its distribution (if known).
(b) What is the probability that a randomly selected MSc graduate has a starting salary less than $50,000?
(c) What is the probability that a sample of 9 randomly selected MSc graduates has an average starting salary between $58,000 and $62,000?
(d) What is the probability that a sample of 32 randomly selected MSc graduates has an average starting salary between $58,000 and $62,000