Let's solve the problem step by step.
Given:
- The mean age of voters, [tex]\(\mu = 65\)[/tex]
- The standard deviation of ages, [tex]\(\sigma = 5\)[/tex]
- The z-score, [tex]\(z_x = 1.14\)[/tex]
We need to find the corresponding age, [tex]\(x\)[/tex], for this z-score. The z-score formula is:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
We can rearrange this formula to solve for [tex]\(x\)[/tex]:
[tex]\[ x = z \cdot \sigma + \mu \][/tex]
Substitute the given values into the formula:
[tex]\[ x = 1.14 \cdot 5 + 65 \][/tex]
Now perform the multiplication:
[tex]\[ x = 5.7 + 65 \][/tex]
Add the values:
[tex]\[ x = 70.7 \][/tex]
Since we are asked to round the answer to the nearest whole number, we round 70.7 to:
[tex]\[ x = 71 \][/tex]
Therefore, the possible voter age that would give a z-score of 1.14 is 71. The correct answer is:
- 71.
