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 proportion of students scored between 81 and 89?
A).0668
B).0132
C).0786
D).0529

Question

Quizplus · Accepted Answer

To solve the problem, we need to standardize the values of 81 and 89 using the formula:

z = (x - μ) / σ

where z is the standardized score, x is the value of interest, μ is the mean, and σ is the standard deviation.

For x = 81:

z = (81 - 69) / 9 = 1.33

For x = 89:

z = (89 - 69) / 9 = 2.22

Next, we look up the area between these Z-scores in the standard normal distribution table or using a calculator:

P(1.33 ≤ Z ≤ 2.22) ≈ 0.0786

Therefore, the proportion of students who scored between 81 and 89 is approximately 0.0786 or 7.86%. Hence the best answer is option C.

A Set of Final Examination Grades in a Calculus Course