A sociology 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 59% C: Scores below the top 41% and above the bottom 23% D: Scores below the top 77% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 70.8 and a standard deviation of 8.6. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

Answer: the minimum score required for an A grade is 81

Step-by-step explanation:

Since the scores on the test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = scores on the test.

µ = mean score

σ = standard deviation

From the information given,

µ = 70.8

σ = 8.6

The probability value for the top 13% of the scores would be (1 - 13/100) = (1 - 0.13) = 0.87

Looking at the normal distribution table, the z score corresponding to the probability value is 1.13

Therefore,

1.13 = (x - 70.8) / 8.6

Cross multiplying by 8.6, it becomes

1.13 * 8.6 = x - 70.8

9.718 = x - 70.8

x = 9.718 + 70.8

x = 81 to the nearest whole number