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 $z_x$ is the z - score, $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Rearrange the formula to solve for $x$

Multiply both sides of the formula 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 $\mu = 65$, $z_x = 1.14$, and $\sigma = 5$. 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:

C. 71