A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 58% C: Scores below the top 42% and above the bottom 25% D: Scores below the top 75% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 78.9 and a standard deviation of 9.3. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

The minimum score required for an A grade is 90.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the minimum score required for an A grade.

Top 12%, so at least the 100-12 = 88th percentile, which is the value of X when Z has a pvalue of 0.88. So it is X when Z = 1.175.

Rounding to the nearest whole number, the answer is 90.

The minimum score required for an A grade is 90.

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step-by-step explanation: