Question

A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. The mean is 74​, with a standard deviation of 8. The teacher wishes to give​ A's to the top 8​% of the students and​ F's to the bottom 8​%. A grade of B is given to the next 16​%, with​ D's given similarly. All other students get​ C's. Find the bottom cutoff for a grade of C.

Answer 1

Explanation:

Given that a teacher gives a test to a large group of students. The results are closely approximated by a normal curve

mu =74 and sigma =8

A grade starts from 100-8 = 92nd percentile

Z score for 92nd percentile = 1.405

X score = 74+8(1.405) = 85.24

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B cut off is to next 16%

Hence C would start for scores below 100-(8+16) = 76%

76th percentile = 0.705*8+74 =79.64