Question

find the data point $x$ given the mean $mu$, standard deviation $sigma$, and a $z$-score.
$mu = 87$
$sigma = 7$
$z=-3$
show your work here

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$. We need to solve for $x$.

Step2: Rearrange the formula for $x$

Multiply both sides of the equation $z=\frac{x - \mu}{\sigma}$ by $\sigma$: $z\sigma=x - \mu$. Then add $\mu$ to both sides to get $x=\mu+z\sigma$.

Step3: Substitute given values

Substitute $\mu = 87$, $\sigma = 7$, and $z=-3$ into the formula $x=\mu+z\sigma$. So $x = 87+(-3)\times7$.

Step4: Calculate the value of $x$

First, calculate $(-3)\times7=-21$. Then $x = 87-21=66$.

Answer:

$66$