Question 1084533: A teacher informs his cell biology class (of 500+ students) that a test was very difficult, but the grades would be curved. Scores on the test were normally distributed with a mean of 26 and a standard deviation of 9. The maximum possible score on the test was 100 points. Because of partial credit, scores were recorded with 1 decimal point accuracy. (Thus, a student could earn a 26.6, but not a 25.31.)
The grades are curved according to the following scheme. Find the numerical limits for each letter grade.
A - Top 8%
B - Scores above the bottom 75%
and below the top 8%
C - Scores above the bottom 25%
and below the top 25%
D - Scores above the bottom 8%
and below the top 75%
F - Bottom 8%
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A teacher informs his cell biology class (of 500+ students) that a test was very difficult, but the grades would be curved. Scores on the test were normally distributed with a mean of 26 and a standard deviation of 9. The maximum possible score on the test was 100 points. Because of partial credit, scores were recorded with 1 decimal point accuracy. (Thus, a student could earn a 26.6, but not a 25.31.)
The grades are curved according to the following scheme. Find the numerical limits for each letter grade.
A - Top 8%
Find the z-score with a left tail of 0.92::
invNorm(0.92) = 1.405
Find the corresponding score::
x = z*s+u
x = 1.405*9+26 = 38.65
Ans: score = 38.7 when rounded up
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B - Scores above the bottom 75%
and below the top 8%
invNorm(0.75) = 0.675
Corresponding score:: 0.675*9+26 = 32.1
Ans:: Above 32.1 ; Below 38.7
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C - Scores above the bottom 25%
and below the top 25%
Above -0.675*9+26 ; Below 0.675*9+26
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Etc.
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Cheers,
Stan H.
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D - Scores above the bottom 8%
and below the top 75%
F - Bottom 8%
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