Question

a data value has a z - score of -2.25. what is the data value if the mean is 30 and the standard deviation is 8?
12
18
22
48

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 data value, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to solve for $x$.

Step2: Rearrange the formula for $x$

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

Step3: Substitute the given values

We are given that $\mu = 30$, $z=-2.25$, and $\sigma = 8$. Substitute these values into the formula $x=\mu+z\sigma$: $x=30+(-2.25)\times8$.

Step4: Perform the calculation

First, calculate $(-2.25)\times8=-18$. Then, $x=30 - 18=12$.

Answer:

12