A college professor teaches corporate finance every semester. The tests for the course are standardized so that the test scores exhibit a normal distribution with a mean of 75 and a standard deviation of 12. The professor gives 15 % A, 25 % B, 30 % C, 20 % D, and 10 % F.

(a) What letter grade will a student who scores 79 points on the test receive?

(b) What letter grade will a student who scores 58 points receive?

(c) How many points does a student need to score to get an A?

(d) How many points does a student need to score to pass the course?