Need help with D highlighted

A set of final examination grades in an introductory statistics course is normallydistributed, with a mean of 71 and a standard deviation of 8. Complete parts(a) through(d).

.a. What is the probability that a student scored below 82 on thisexam?

The probability that a student scored below 82 is

0.9162

0.9162.

(Round to four decimal places asneeded.)

b. What is the probability that a student scored between 63 and 94?

The probability that a student scored between 63 and 94 is

0.8393

0.8393.

(Round to four decimal places asneeded.)

c. The probability is 15% that a student taking the test scores higher than whatgrade?

The probability is 15% that a student taking the test scores higher than

79

79.

(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 87 on the exam with a mean of 71 and a standard deviation of 8 or a grade of 64 on a differentexam, where the mean is 61 and the standard deviation is 3? Show your answer statistically and explain.

A student is worse off/better off with a grade of 87 on the exam with a mean of 71 and a standard deviation of 8 because the Z value for the grade of 87 is and the Z value for the grade of 64 on the different exam is

.

(Round to two decimal places asneeded.)