Sally's z-score on a given measure is -2.5, where the population mean is 5 and the standard deviation is 1.5.What is Sally's raw score?
A)1.25
B)14
C)3.5
D)8.75

Question

Quizplus · Accepted Answer

Sally's raw score can be calculated using the formula for a z-score: $Z = \frac{(X - \mu)}{\sigma}$, where $Z$ is the z-score, $X$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation. Rearranging the formula to solve for $X$ gives $X = Z\sigma + \mu$. Plugging in Sally's z-score (-2.5), the mean (5), and the standard deviation (1.5) gives $X = -2.5(1.5) + 5 = -3.75 + 5 = 1.25$.

Sally's Z-Score on a Given Measure Is -2