A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 76.5 and a standard deviation of 9. If 67.36% of his students received grades of C or above,what is the minimum score of those students receiving a grade of at least a C?
A)67.36
B)72.45
C)66.56
D)70.00

Question

Quizplus · Accepted Answer

First, we need to find the z-score corresponding to the 67.36 percentile using a standard normal distribution table or calculator. The closest z-score corresponding to this percentile is 0.44.

Next, we use the formula for z-score:

z = (x - μ) / σ

where x is the minimum score for a grade of at least C, μ is the mean (76.5), and σ is the standard deviation (9).

We rearrange the formula to find x:

x = z*σ + μ

Plugging in the values, we get:

x = 0.44 * 9 + 76.5

x ≈ 79.05

Therefore, the minimum score for a grade of at least C is approximately 79.05. The closest choice is B, 72.45, which is not the correct answer.

A College Professor Noted That the Grades of His Students