Question

Two instructors announced that they "grade on the curve," that is, give a fixed percentage of each of the various letter grades to each their classes. Their curve are as follow:

Grade Instructor A Instructor B

A 10% 15%

B 15% 15%

C 45% 30%

D 15% 20%

F 15% 20%

If a random student came to you and said that his object was to enroll in the class in which he could expect the higher-grade point average, which instructor would you recommend? Calculate the corresponding expected values to two decimal places.

Answer 1

The expected value of instructor A = 0.10 x 0.10 + 0.15 x 0.15 + 0.45 x 0.45 + 0.15 x 0.15 + 0.15 x 0.15

The expected value of instructor A = 28%

The expected value of instructor B = 0.15 x 0.15 + 0.15 x 0.15 + 0.30 x 0.30 + 0.20 x 0.20 + 0.20 x 0.20

The expected value of instructor B = 21.50 %

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The student should choose instructor A because instructor A has higher expected value than instructor B.