A psychology professor assigns letter grades on a test according to the following scheme. A: Top 11% of scores Scores on the test are normally distributed with a mean of 71.9 and a standard deviation of 8.4 . Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

Answer 1

To find the minimum score required for an A grade, we need to find the z-score that corresponds to the top 11% of scores.

Using the normal distribution table, we find that the z-score for the top 11% of scores is approximately 1.23.

Next, we can use the formula for z-score to find the corresponding raw score:

z = (X - μ) / σ

Rearranging the formula to solve for X, we have:

X = z * σ + μ

Plugging in the values, we get:

X = 1.23 * 8.4 + 71.9 ≈ 81.3

Therefore, the minimum score required for an A grade is approximately 81.3. Rounded to the nearest whole number, the minimum score required for an A grade is 81.