A set of scores has a standard deviation of 6. A raw score of 53 converts to a z-score of -1.5. What is the mean of the distribution?
A) 56
B) 62
C) 65
D) 51.5

Question

Quizplus · Accepted Answer

The formula for calculating a z-score is $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the given values, $-1.5 = \frac{(53 - \mu)}{6}$. Solving for $\mu$ gives $\mu = 62$.

A Set of Scores Has a Standard Deviation of 6