Professor Moriarty has never taken a formal statistics course; however, he has h

ID: 3042841 • Letter: P

Question

Professor Moriarty has never taken a formal statistics course; however, he has heard about the bell-shaped curve and has some knowledge of the Empirical Rule for normal distributions. Professor Moriarty teaches as Honors Quantum Physics class in which he grades on the bell curve. He assigns letter grades to his students' tests by assuming a normal distribution and utilizing the Empirical Rule. The Professor reasons that if IQ and SAT scores follow a normal distribution, then his students' scores must do so also. Therefore, upon scoring the tests, he determines the mean and standard deviation for his class. He then uses the Empirical Rule to assign letter grades so that 68% of the students receive a "C," 95% receive "B-D," and 99.7% receive "A-F."

The following test grades occur on the midterm exam for his class: 78 85 93 62 82 76 74 73 91 66 89 88 86 94 65 90 84 92 94 92 82 85 80 77 52 84 78 83

a) You are working as Professor Moriarty's graduate assistant and he has asked that you use the Empirical Rule to determine which of these grades he should assign as "A," "B," "C," "D," and "F." After finding the mean and standard deviation for the midterm grades, give the interval of test scores that will qualify for each letter category. (In other words, what range of scores will earn an "A," "B," and so on?) Also give how many students will earn each letter grade using this grading scheme.

b) Determine the number of students who would receive an "A," "B," "C," "D," and "F" using a standard grading scheme where 90-100 earns an "A," 80-89 earns a "B," 70-79 earns a "C," 65-69 earns a "D," and below 65 earns an "F." Describe this grade distribution and contrast it with the one that results from using the bell curve

That is for the normal ranges for part b. What about part a? How many made A's? What is the A range?

Explanation / Answer

The ranges of One Sigma, Two Sigma and Three Sigma limits are given in following table:

Lower

Upper

1 Sigma Limit

70.82

92.40

2 Sigma Limit

60.02

103.19

3 Sigma Limit

49.23

113.98

Thus students with score,

Between 103.19 to 113.98 will receive grade A, it will receive to 2.14 % students

Between 92.40 to 103.19 will receive grade B, it will receive to 13.60 % students

Between 70.82 to 92.40 will receive grade C, it will receive to 68.27 % students

Between 60.02 to 70.82 will receive grade D, it will receive to 13.60 % students

Between 49.23 to 60.02 will receive grade F, it will receive to 2.14 % students

Score

Grade

% Students

90-100

17.43

80-89

34.09

70-79

29.97

65-69

7.91

< 65

10.60