Question

a missing data value from a set of data has a z - score of - 2.1. fred already calculated the mean and standard deviation to be $mu = 43$ and $sigma = 2$. what was the missing data value? round the answer to the nearest whole number.
39
41
45
47

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 $x$

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 the given values

We are given that $\mu = 43$, $z=-2.1$, and $\sigma = 2$. Substitute these values into the formula $x=\mu+z\sigma$: $x=43+(-2.1)\times2$.

Step4: Calculate the value of $x$

First, calculate $(-2.1)\times2=-4.2$. Then, $x=43 - 4.2=38.8$.

Step5: Round the result

Rounding $38.8$ to the nearest whole number gives $39$.

Answer:

A. 39