Question

one hundred students wrote an exam. the average was 12.8 and the standard deviation was 1.8. the standard error of the mean was 6. if a students actual score was 8.5, what is the students z-score?
a. 11.83
b. -3.21
c. 2.39
d. -2.39

Explanation:

Step1: Recall z-score formula

The z-score formula is $z = \frac{X - \mu}{\sigma}$, where $X$ is the individual score, $\mu$ is the population mean, and $\sigma$ is the population standard deviation. (Note: The standard error of the mean is irrelevant for calculating an individual's z-score.)

Step2: Plug in given values

Substitute $X=8.5$, $\mu=12.8$, $\sigma=1.8$ into the formula:
$z = \frac{8.5 - 12.8}{1.8}$

Step3: Calculate numerator first

$8.5 - 12.8 = -4.3$

Step4: Compute final z-score

$z = \frac{-4.3}{1.8} \approx -2.39$

Answer:

d. -2.39