Suppose that college faculty with the rank of professor at two-year institutions earn an average of $64,571 per year with a standard deviation of $4,000. In an attempt to verify this salary level, a random sample of 60 professors was selected from a personnel database for all two-year institutions inthe United States and the average salary xwas calculated.

(1)Describe the sampling distribution of the sample mean x

(2)Within what limits would you expect the sample average to lie, with probability 0.95?

(3)If your random sample actually produced a sample mean of $66,000, would you consider this unusual? What conclusion might you draw? Hint: what is the probability of observing a samplemean larger than this?