Question

a group of scores has mean equal to 55. a raw score of 50 corresponds to a z score of -1. what is the standard deviation of these scores?

a. cant be determined with the information provided
b. -5
c. 5
d. 1
e. -1

Explanation:

Step1: Recall Z-score formula

The Z-score formula is $Z = \frac{X - \mu}{\sigma}$, where $Z$ is the Z-score, $X$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Plug in known values

Substitute $Z=-1$, $X=50$, $\mu=55$ into the formula:
$-1 = \frac{50 - 55}{\sigma}$

Step3: Simplify numerator

Calculate $50 - 55 = -5$, so:
$-1 = \frac{-5}{\sigma}$

Step4: Solve for $\sigma$

Rearrange the equation to isolate $\sigma$:
$\sigma = \frac{-5}{-1} = 5$

Answer:

c. 5