Question

on a recent quiz, a class mean was 72 with a standard deviation of 8.2. grading was done on a curve so the scores were roughly bell shaped. calculate the z - score (to 2 decimal places) for a person who received a score of 90.
z - score:
would getting a score of 90 be considered 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 data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 72$, $\sigma=8.2$, and $x = 90$.

Step3: Calculate z - score

Substitute the values into the formula: $z=\frac{90 - 72}{8.2}=\frac{18}{8.2}\approx2.20$.

A z - score is considered unusual if $|z|> 2$. Since $z = 2.20>2$, a score of 90 is unusual.

Answer:

z - score: 2.20
Would getting a score of 90 be considered unusual/significant? Unusual/Significant