To determine the possible voter age corresponding to a [tex]\( z \)[/tex]-score of 1.14 given the mean ([tex]\(\mu\)[/tex]) and standard deviation ([tex]\(\sigma\)[/tex]), we can use the formula for the [tex]\( z \)[/tex]-score, which is:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
Here:
- [tex]\( z \)[/tex] is the [tex]\( z \)[/tex]-score,
- [tex]\( X \)[/tex] is the voter age we are trying to find,
- [tex]\(\mu\)[/tex] is the mean age, which is 65,
- [tex]\(\sigma\)[/tex] is the standard deviation, which is 5.
We need to solve for [tex]\( X \)[/tex]. Rearranging the equation to solve for [tex]\( X \)[/tex]:
[tex]\[ X = z \cdot \sigma + \mu \][/tex]
Substitute the given values into the equation:
[tex]\[ X = 1.14 \cdot 5 + 65 \][/tex]
Calculate the multiplication:
[tex]\[ X = 5.7 + 65 \][/tex]
Add the results:
[tex]\[ X = 70.7 \][/tex]
Since we need to round the answer to the nearest whole number, 70.7 rounds up to 71.
Therefore, a possible voter age that would give a [tex]\( z \)[/tex]-score of 1.14 is 71. The correct answer is 71.
