Question

a poll worker analyzing the ages of voters found that $mu = 65$ and $sigma = 5$. what is a possible voter age that would give her $z_x=1.14$? round your answer to the nearest whole number.
59
66
71
90

Explanation:

Step1: Recall z - score formula

The z - score formula is $z_x=\frac{x - \mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We need to solve for $x$.

Step2: Rearrange the formula for $x$

Starting from $z_x=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$: $z_x\sigma=x - \mu$. Then add $\mu$ to both sides to get $x=\mu+z_x\sigma$.

Step3: Substitute the given values

We are given that $\mu = 65$, $\sigma = 5$, and $z_x = 1.14$. Substitute these values into the formula: $x=65+1.14\times5$.

Step4: Calculate the value of $x$

First, calculate $1.14\times5 = 5.7$. Then $x=65 + 5.7=70.7$.

Step5: Round to the nearest whole number

Rounding $70.7$ to the nearest whole number gives $71$.

Answer:

71