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[From: ] [author: ] [Date: 11-04-22] [Hit: ]
A: 69 + (1.29 · 12.B: 69 + (.26 · 12.C: 69 + (-.26 · 12.......
A Mathematics Professor assigns letter grades on a test according to the following scheme:

A: Top 10%

B: Scores below the top 10% and above the bottom 60%

C: Scores below the top 40% and above the bottom 20%

D: Scores below the top 80% and above the bottom 10%

F: Bottom 10%

Scores on the test are normally distributed with a mean of 69 and a standard deviation of 12.4.
Find the numerical limits for each letter grade.

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To do this you need the z score for the appropriate percentiles.

The z for the 90th percentile (top 10%) is 1.29
The z for the 60th percentile is .26
The z for the 40th percentile is -.26
The z for the 20th percentile is -.85
The z for the 10th percentile is -1.29

Given those, then you need to calculate the numerical limits using the mean and standard deviation:
Limit = µ + (z · σ)

The lower limits for each grade are:
A: 69 + (1.29 · 12.4) = 85
B: 69 + (.26 · 12.4) = 72
C: 69 + (-.26 · 12.4) = 66
D: 69 + (-.85 · 12.4) = 58
F: 69 + (-1.29 · 12.4) = 53
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