the average score on the first - midterm was 70 points with a standard deviation of 7 points, and gregors z…

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 know that $\mu = 70$, $\sigma=7$, and $z = 3$.

Step2: Rearrange the formula to solve 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 the given values

Substitute $\mu = 70$, $z = 3$, and $\sigma = 7$ into the formula $x=\mu+z\sigma$. So $x=70+3\times7$.

Step4: Calculate the value of $x$

$x=70 + 21=91$.

Answer:

91