4. The grades on the midterm examination given in a large managerial statistics

Question

4. The grades on the midterm examination given in a large managerial statistics class are normally distributed with mean 75 and standard deviation 9. The instructor of this class wants to assign an A grade to the top 25% of the scores, a B grade to the next 40% of the scores, a C grade to the next 15% of the scores, a D grade to the next 10% of the scores, and an F grade to all scores in the bottom 10% of this distribution. For each possible letter grade, find the lowest acceptable score within the established range.

Explanation / Answer

Here from the standard normal tables, we first compute the z scores for the lowest acceptable score for each grade and then using the z-score the mid term test score is computed using:

X = Mean + Z*Std Dev.

The lowest acceptable score for each grade is computed in the last column.

Grade Condition Z score Lowest Acceptable Score A Top 25% P(Z > 0.6745 ) = 0.25 75 + 0.25*9 = 77.25 B Next 40% P(Z > -0.3853 ) = 0.65 75 -0.3853*9 = 71.5323 C Next 15% P(Z > -0.8416 ) = 0.80 75 -0.8416*9 = 67.4256 D Next 10% P(Z > -1.282 ) = 0.90 75 -1.282*9 = 63.462 F Bottom 10% Not required Could be as low as poissble

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