25. Faculty Salaries Suppose that college faculty with the rank of professor at public 2-year institutions earn an average of $75,878 per year7 with a standard deviation of $4000. In an attempt to verify this salary level, a random sample of 60 professors was selected from an appropriate database.

a. Describe the sampling distribution of the sample mean x.

b. Within what limits would you expect the sample average to lie, with probability .95?

c. Calculate the probability that the sample mean x is greater than $78,000?

d. If your random sample actually produced a sample mean of $78,000, would you consider this unusual?
What conclusion might you draw?