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A poll worker analyzing the ages of voters found that [tex]\mu = 65[/tex] and [tex]\sigma = 5[/tex]. What is a possible voter age that would give her [tex]z_x = 1.14[/tex]? Round your answer to the nearest whole number.

A. 59
B. 66
C. 71
D. 90


Sagot :

To determine a possible voter age that corresponds to a z-score of [tex]\( z_x = 1.14 \)[/tex] given a mean ([tex]\(\mu\)[/tex]) of 65 and a standard deviation ([tex]\(\sigma\)[/tex]) of 5, follow these steps:

1. Recall the Z-score formula:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
where:
- [tex]\( z \)[/tex] is the z-score
- [tex]\( x \)[/tex] is the value for which we are calculating the z-score
- [tex]\( \mu \)[/tex] is the mean
- [tex]\( \sigma \)[/tex] is the standard deviation

2. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = z \cdot \sigma + \mu \][/tex]
Here, [tex]\( z_x = 1.14 \)[/tex], [tex]\(\mu = 65\)[/tex], and [tex]\(\sigma = 5 \)[/tex].

3. Substitute the values given:
[tex]\[ x = 1.14 \cdot 5 + 65 \][/tex]

4. Calculate the result:
[tex]\[ x = 5.7 + 65 \][/tex]
[tex]\[ x = 70.7 \][/tex]

5. Round [tex]\( x \)[/tex] to the nearest whole number:
[tex]\[ 70.7 \approx 71 \][/tex]

Therefore, a possible voter age that would give a z-score of [tex]\( z_x = 1.14 \)[/tex] is 71.