Question

the average score on the stats mid - term was 72 points with a standard deviation of 6 points, and gregors z - score was 1. how many points did he score? he scored □ points.

Explanation:

Step1: Recall z - score formula

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

Step2: Rearrange the formula for $x$

Starting from $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$: $z\sigma=x - \mu$. Then add $\mu$ to both sides to get $x=\mu+z\sigma$.

Step3: Substitute given values

We are given that $\mu = 72$, $\sigma = 6$, and assume a common value for $z$ (since it's not given in the visible part of the problem, if we assume a typical case where $z = 1$ for illustration purposes). Then $x=72 + 1\times6$.
$x=72 + 6=78$.

Answer:

78 (assuming $z = 1$. If a different $z$ - score value is given, substitute it into the formula $x=\mu+z\sigma$ for the correct answer)