Question

A humanities 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 60% C: Scores below the top 40% and above the bottom 24% D: Scores below the top 76% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 65.1 and a standard deviation of 9.2. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

Answer 1

Here' the answer to the question. please write back in case you've doubts.

A minimum score to get an A grade would mean that such a score "a" will have P(X > a) = .13

So, lets find a such that P(X>a) = .13

or P(X<=a) = 1-.13 = .87

Now, the Z score ( using Ztable ) fro .87 cumulative probability is 1.2264.

We will standardize the distribution by given normal distribution parameters:

Mean = 65.1, Stdev = 9.2

So, (a-65.1)/9.2 = 1.2264

a = 1.2264*9.2 + 65.1 = 75.33 or 75 ( rounding off to nearest whole number)

Answer is 75