According to The Chronicle of Higher Education, 69% of MBA graduates in 2007-8 had some student loan debt when they graduated. An administrator claims that the percentage of MBA graduates with student loan debt is the same at your university. To test the claim, a simple random sample of 25 MBA graduates is taken. Assume the administrator's claim is correct.
a. What is the probability that exactly 18 of the graduates in the sample have some student loan debt?
b. What is the probability that more than 20 graduates in your sample have some student loan debt?
c. Suppose that when the sample is taken, 21 of the 25 graduates have some student loan debt. Do you believe the administrator's claim? Explain why or why not using probabilities.