A set of final examination grades in an introductory statistics course is normallydistributed, with a mean of 79 and a standard deviation of 7. Complete parts(a) through(d).

a. What is the probability that a student scored below 87 on thisexam?

The probability that a student scored below 87 is

.(Round to four decimal places asneeded.)

b. What is the probability that a student scored between 72 and 98?

The probability that a student scored between 72 and 98 is

.

(Round to four decimal places asneeded.)

c. The probability is 25% that a student taking the test scores higher than whatgrade?

The probability is 25% that a student taking the test scores higher than

.

(Round to the nearest integer asneeded.)

d. If the professor grades on a curve(for example, the professor could giveA's to the top10% of theclass, regardless of thescore), is a student better off with a grade of 93 on this exam or a grade of 71 on a differentexam, where the mean is 67 and the standard deviation is 4? Show your answer statistically and explain.

A student is better off/worse off with a grade of 93 on this exam because the Z value for the grade of 93 is and the Z value for the grade of 71 is

.

(Round to two decimal places asneeded.)