A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What percentage of students scored between 81 and 89?
A).0668
B).0132
C).0536
D).0529

Question

Quizplus · Accepted Answer

First, we need to standardize the scores using the z-score formula:

z = (x - μ) / σ

For x = 81:

z = (81 - 69) / 9 = 1.33

For x = 89:

z = (89 - 69) / 9 = 2.22

Next, we use a standard normal distribution table or calculator to find the area between these two z-scores:

P(1.33 ≤ Z ≤ 2.22) = 0.0536

Therefore, 5.36% of students scored between 81 and 89. The closest answer choice is (C) 0.0536.

A Set of Final Examination Grades in a Calculus Course