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.
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.

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
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