The National Center for Educational Statistics reported that 82% of freshmen entering public high schools in the U.S. in 2009 graduated with their class in 2013.

A random sample of 135 freshmen is chosen.

a. Find the mean μp̂.

b. Find the standard deviation σp̂

c. Find the probability that less than 80% of freshmen in the sample graduated.

d. Find the probability that the sample proportion of students who graduated is between 0.75 and 0.85.

e. Find the probability that more than 75% of freshmen in the sample graduated.

f. Would it be unusual if the sample proportion of students who graduated were more than 0.90?