Question

a poll worker analyzing the ages of voters found that μ = 65 and σ = 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 formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $z$ is the z - score, $x$ is the raw score (voter age in this case), $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $z = 1.14$, $\mu=65$, and $\sigma = 5$. We need to solve for $x$.

Step2: Rearrange the formula to solve for x

Starting with $z=\frac{x - \mu}{\sigma}$, multiply both sides by $\sigma$: $z\times\sigma=x-\mu$. Then add $\mu$ to both sides: $x=\mu+z\times\sigma$.

Step3: Substitute the values

Substitute $\mu = 65$, $z = 1.14$, and $\sigma=5$ into the formula: $x=65 + 1.14\times5$. First, calculate $1.14\times5=5.7$. Then, $x=65 + 5.7=70.7\approx71$.

Answer:

71