A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8.

a. What is the probability that a student scored below 91 on this exam?

b. What is the probability that a student scored between 65 and 89?

c. The probability is five percent that a student taking the test scores higher than what grade?

d. If the professor grades on a curve (i. e., gives As to the top ten percent of the class, regardless of the score), are you better off with a grade of 81 on this exam or a grade of 68 on a different exam, where the mean is 62 and the standard deviation is 3? Show your answer statistically and explain.