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A humanities 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 63% C: Scores below the top 37% and above the bottom 16% D: Scores below the top 84% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 80.1 and a standard deviation of 7.2. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

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Answer: 88.56

Step-by-step explanation:

Given that:

Mean score (m) = 80.1

Standard deviation (s) = 7.2

Minimum score required to score A grade =?

A= Top 12% of scores

Zscore corresponding to top 12% = bottom 88%

Zscore = 1.175

Zscore = (x - mean) / s

1.175 = (x - 80.1) / 7.2

1.175 * 7.2 = x - 80.1

8.46 = x - 80.1

8.46 + 80.1 = x

x = 88.56

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