Question

1. harry scored 10.06 in his test, in which the mean was 5.9 and the standard deviation was 1.6. roxanne scored 27.1 in her test, in which the mean was 15.9 and the standard deviation was 2.8. 8a find harrys z - score. z = 2.6 8b find roxannes z - score. z =

Explanation:

Step1: Recall z-score formula

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

Step2: Plug in Roxanne's values

Substitute $x=27.1$, $\mu=15.9$, $\sigma=2.8$ into the formula:
$z = \frac{27.1 - 15.9}{2.8}$

Step3: Calculate numerator first

$27.1 - 15.9 = 11.2$

Step4: Compute final z-score

$z = \frac{11.2}{2.8} = 4$

Answer:

$z = 4$