A psychology professor assigns letter grades on a test according to the following scheme. A: Top 11% of scores B: Scores below the top 11% and above the bottom 61% C: Scores below the top 39% and above the bottom 16% D: Scores below the top 84% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 81.8 and a standard deviation of 7.8. 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 91

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 = 81.8

σ = 7.8

The probability value for the scores in the top 11% would be (1 - 11/100) = (1 - 0.11) = 0.89

Looking at the normal distribution table, the z score corresponding to the probability value is 1.23

Therefore,

1.23 = (x - 81.8) / 7.8

Cross multiplying by 114, it becomes

1.23 * 7.8 = x - 81.8

9.594 = x - 81.8

x = 9.594 + 81.8

x = 91 rounded to the nearest whole number.