Question

a data value has a z - score of 3.15. what is the data value if the mean is 20 and the standard deviation is 4? 7.4 27.4 12.6 32.6

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 $\mu = 20$, $z = 3.15$, and $\sigma=4$. Substitute these values into the formula $x=\mu + z\sigma$. So $x=20+3.15\times4$.

Step4: Calculate the value of $x$

First, calculate $3.15\times4 = 12.6$. Then, $x=20 + 12.6=32.6$.

Answer:

D. 32.6