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rofessor Moriarty has never taken a formal statistics course;however, he has heard about the bell-shaped curve and has someknowledge of the Empirical Rule for normal distributions. ProfessorMoriarty teaches as Honors Quantum Physics class in which he gradeson the bell curve. He assigns letter grades to his students' testsby assuming a normal distribution and utilizing the Empirical Rule.The Professor reasons that if IQ and SAT scores follow a normaldistribution, then his students' scores must do so also. Therefore,upon scoring the tests, he determines the mean and standarddeviation for his class. He then uses the Empirical Rule to assignletter 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 hisclass: 78 85 93 62 82 76 74 73 91 66 89 88 86 94 65 90 84 92 94 9282 85 80 77 52 84 78 83

a) You are working as Professor Moriarty's graduate assistantand he has asked that you use the Empirical Rule to determine whichof these grades he should assign as "A," "B," "C," "D," and "F."After finding the mean and standard deviation for the midtermgrades, give the interval of test scores that will qualify for eachletter category. (In other words, what range of scores will earn an"A," "B," and so on?) Also give how many students will earn eachletter 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 90-100earns 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 distributionand contrast it with the one that results from using the bellcurve.

c) As a student of statistics, you have some concerns aboutProfessor Moriarty's use of the normal distribution in thiscontext. Discuss your concerns with your classmates. Why might hispractice not be statistically sound? Provide statistical evidenceto support your position so that you can justify your argumentagainst this method of grading. (Statistical evidence could includemeasures of relative position, charts or tables, explanationssupported by statistical knowledge or analysis, etc.)