A professor noted that the grades of his students were normally distributed with a mean of 75.07 and a standard deviation of 11.65. If only 10 percent of the students received grades of A, what is the minimum score needed to receive an A?
A) 80.00
B) 85.00
C) 90.00
D) 95.00

Question

Quizplus · Accepted Answer

To find the minimum score needed to receive an A (top 10% of the grades), we use the concept of z-scores in a normal distribution. The z-score corresponding to the top 10% (90th percentile) is approximately 1.28. Using the formula for a z-score: $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation, we can solve for $X$. Plugging in the values: $1.28 = \frac{(X - 75.07)}{11.65}$, solving for $X$ gives a score slightly above 89, which means the minimum score needed to receive an A is closest to 90.

A Professor Noted That the Grades of His Students Were