SOLUTION: An English 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

Question 1146568: An English 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 22%
D: Scores below the top 78% and above the bottom 6%
F: Bottom 6% of scores
Scores on the test are normally distributed with a mean of 75.1 and a standard deviation of 9.1. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
use the following calculator and your job gets much easier.

http://davidmlane.com/hyperstat/z_table.html

to get a grade of D, your score must be below the top 78% and above the bottom 6%.

to find the raw scores, you set the mean to 75.1 and the standard deviation to 9.1.

you then select value from an area.

the raw score associated with 6% of the area under the normal distribution curve being to the left of it (below) would be equal to 60.952.

the raw score associated with 78% of the area under the normal distribution curve being to the right of it (above) would be equal to 68.073.

to get a D, the student must get a score greater than 60.952 and less than 68.073.

round to the nearest whole number and the student needs to get a score between 61 and 68.

the inputs and outputs from the use of the calculator are shown below.

$$$

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