A professor would like to assign grades such that 5% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)
A) 80
B) 83
C) 90
D) 93

Question

Quizplus · Accepted Answer

To find the cutoff for an A, we need to find the score that separates the top 5% of the students from the rest of the class. We can use the standard normal distribution table to do this.

First, we need to find the z-score corresponding to the top 5% of the distribution. This is the z-score that has an area of 0.05 to the right of it. From the table, we find that the z-score corresponding to the top 5% is 1.645.

Next, we use the formula for converting a raw score to a z-score:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation. Rearranging the formula, we can solve for x:

x = z * σ + μ

Plugging in the values we have, we get:

x = 1.645 * 13 + 62
x = 83.485

So a score of 83 or higher should receive an A. The closest answer choice is B, 83.

A Professor Would Like to Assign Grades Such That 5