A statistics student receives a grade of 85 on a statistics midterm. If the corresponding z-score equals +1.5 and the standard deviation equals 7, the average grade on this exam is _______.
A) 74.5
B) 75.4
C) 68.5
D) 76.9

Question

Quizplus · Accepted Answer

The z-score formula is $Z = \frac{(X - \mu)}{\sigma}$, where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. Rearranging to solve for $\mu$, we get $\mu = X - Z\sigma$. Plugging in the given values, $\mu = 85 - (1.5 \times 7) = 85 - 10.5 = 74.5$.

A Statistics Student Receives a Grade of 85 on a Statistics