Question

janices teacher told her that her z - score for her grade on the science test was 2. if janice scored an 84, and the class standard deviation was 4, what was the class mean?

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 individual score, $\mu$ is the mean, and $\sigma$ is the standard deviation.
We know that $z = 2$, $x=84$, and $\sigma = 4$.

Step2: Rearrange the formula to solve for the mean

Starting with $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$: $z\sigma=x - \mu$.
Then, we can rewrite it to solve for $\mu$: $\mu=x - z\sigma$.

Step3: Substitute the known values

Substitute $x = 84$, $z = 2$, and $\sigma = 4$ into the formula $\mu=x - z\sigma$.
$\mu=84-2\times4$.
First, calculate $2\times4 = 8$.
Then, $84−8 = 76$.

Answer:

76