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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 :

GinnyAnswer
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.
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