Question

1. a set of test scores has a mean of 82. if you earned a 90% on the test and a z - score of 1.6, what is the standard deviation?

Explanation:

Step1: Recall the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $z$ is the z - score, $x$ is the individual value, $\mu$ is the mean, and $\sigma$ is the standard deviation.
We know that $z = 1.6$, $x=90$, and $\mu = 82$.

Step2: Rearrange the formula to solve for $\sigma$

Starting with $z=\frac{x - \mu}{\sigma}$, we can cross - multiply to get $z\sigma=x-\mu$. Then $\sigma=\frac{x - \mu}{z}$.

Step3: Substitute the known values into the formula

Substitute $x = 90$, $\mu=82$, and $z = 1.6$ into $\sigma=\frac{x - \mu}{z}$.
$\sigma=\frac{90 - 82}{1.6}$
$=\frac{8}{1.6}$
$ = 5$

Answer:

5