Question

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 56% c: scores below the top 44% and above the bottom 20% d: scores below the top 80% and above the bottom 9% f: bottom 9% of scores scores on the test are normally distributed with a mean of 78.6 and a standard deviation of 9.5 . find the minimum score required for an a grade. round your answer to the nearest whole number, if necessary.

Answer 1

90

Explanation:

You want the nearest whole number to the boundary at the 88th percentile in a normal distribution with a mean of 78.6 and a standard deviation of 9.5.

88th percentile

Standard functions are available for finding the value corresponding to a given area under the normal probability density curve. Here, we want the value such that 12% of the area is above that value. It means 88% will be below the value. This is called the 88th percentile of the distribution.

The attached calculator output shows the test score for a letter grade of A must be at least 90.