Question

on a recent quiz, the class mean was 74 with a standard deviation of 3.2. calculate the z - score (to 2 decimal places) for a person who received score of 71.
z - score:
is this unusual/significant?
not unusual/not significant
unusual/significant

Explanation:

Step1: Recall z - score formula

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

Step2: Identify values

We are given that $\mu = 74$, $\sigma=3.2$, and $x = 71$.

Step3: Substitute values into formula

$z=\frac{71 - 74}{3.2}=\frac{- 3}{3.2}=-0.94$ (rounded to 2 decimal places).

Step4: Determine significance

Typically, if $|z|\lt2$, the value is not considered unusual. Since $| - 0.94|\lt2$, it is not unusual.

Answer:

z - score: - 0.94
Not Unusual/Not Significant