Final averages are typically approximately normally distributed with a mean of 66 and a standard deviation of 10.5. Your professor says that the top 5% of the class will receive an A; the next 15%, a B; the next 47%, a C; the next 22%, a D; and the bottom 11%, an F.

Question

Final averages are typically approximately normally distributed with a mean of 66 and a standard deviation of 10.5. Your professor says that the top 5% of the class will receive an A; the next 15%, a B; the next 47%, a C; the next 22%, a D; and the bottom 11%, an F.
(a) What average must you exceed to obtain an A?

(b) What average must you exceed to receive a grade of C or better?

(c) What average must you obtain to pass the course? (You'll need a D or better.)