The grades on the final examination given in a large organic chemistry class are

Question

The grades on the final examination given in a large organic chemistry class are normally distributed with a mean of 72 and a standard deviation of 8. The instructor of this class wants to assign an “A” grade to the top 10% of the scores, a “B” grade to the next 10% of the scores, a “C” grade to the next 10% of the scores, a “D” grade to the next 10% of the scores, and an “F” grade to all scores below the 60th percentile of this distribution. For a letter grade of C, find the lowest acceptable score within the established range. Provide your answer in the format XX.X, for example 83.4.

Explanation / Answer

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The normal distribution' params are Mean = 72 Stdev = 8

A has top 10% or a Z score of +1.28. So to get an A you must have:

Mean + Z*Stdev = 72+1.28*8 = 82.24

You must score 82.2 or above to get an A

The next 10% or from 80% to 90% will get a B. So, to get a B you must score within a range of Z = .842 to 1.28

So,

Mean + Z*Stdev = (72+.842*8) to (72+1.28*8) = 82.24 - 78.84 to 82.2

You must score with the above range to get B

A C will be within 70% to 80% or (72+.52*8) to  (72+.842*8) = 76.2 to 78.8

A D will be within 60% to 70% or (72+.25*8) to  (72+.52*8) = 74 to 76.2

A F will be below 60% or below (72+.25*8) = below 74

So, for a C the lowest accptance score is (least within 60% and 70% ) = 74

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