A sociology professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 61% C: Scores below the top 39% and above the bottom 20% D: Scores below the top 80% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 73.5 and a standard deviation of 7.9 Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
To find the minimum score for A grade:
= mean = 73.5
= SD = 7.9
A grade: Top 13% of scores.
Top 13% corresponds to area = 0.50 - 0.13 = 0.37 from mid value to Z on RHS.
Table of Area Under Standard Normal Curve gives Z score corresponding to area = 0.37 as Z = 1.13
So,
Z = 1.13 = (X - 73.5)/7.9
So,
X = 73.5 + (1.13 X 7.9)
= 82.427
= 82 (Round to the nearest whole number)
So,
Answer is:
82
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