The Dean of Nursing tells students being recruited for the incoming class that 1 year after graduation, the university’s graduates can expect to be earning a mean weekly income of $675. Assume that the dean’s statement is true and that the weekly salaries 1 year after graduation are normally distributed with a standard deviation of $85.

If one graduate is randomly selected:

a. Describe the distribution of the weekly salaries being earned 1 year after graduation.

b. What is the probability that the selected graduate is making between $550 and $825?
If a random sample of 25 graduates is selected:

c. Describe the distribution of mean weekly salaries being earned 1 year after graduation.

d. What is the probability that the sample mean is between $650 and $705?

e. Why is the z-score used in answering parts b and d?

f. Why is the formula for z-score used in part d different from that used in part b?