SOLUTION: An art history 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 56% C: Scor

Question 1119173: An art history 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 56%
C: Scores below the top 44% and above the bottom 21%
D: Scores below the top 79% and above the bottom 9%
F: Bottom 9% of scores
Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
top 13% is z=+1.128
z=(x-mean)/sd=(x-79.7)/8.4=1.128
score=89.18 or 89
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bottom 56% is 44th percentile and z=-0.15
score is (x-79.7)=-.15*8.4
=78.4 or 78
range is [78, 89]
-----------------
Below top 44 and above the bottom 21
The top 44 are above z=+0.15 or a score of 80.96 or 81
Bottom 21% are at z of -0.81 or a score of 72.90 or 73
so range is [73, 81]
Top 79% are above the 21st percentile so any score below 73 is below the top 79%. The bottom 9% are with z=-1.34 so -1.34=(x-79.7)/8.4
-11.26=x-79.7, so this score is 68.44 or 68
[68, 73]
Bottom 9% is <68

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