Question

a data value has a z - score of -2.1. what is the data value if the mean is 20 and the standard deviation is 4? 11.6 8.4 28.4 11.2

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 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 $\mu = 20$, $z=-2.1$, and $\sigma = 4$. Substitute these values into the formula $x=\mu+z\sigma$. So $x=20+(-2.1)\times4$.

Step4: Calculate the value of $x$

First, calculate $(-2.1)\times4=-8.4$. Then $x = 20-8.4=11.6$.

Answer:

A. 11.6