Question

age of senators the average age of senators in the 108th congress was 61 years. if the standard deviation was 11.5 years, find the z - scores corresponding to the oldest and youngest senators of age 84 and 39. round z scores to two decimal places.
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part 1 of 2
the z - score corresponding to the oldest senator of age 84 is .

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value from the dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values for oldest senator

For the oldest senator, $x = 84$, $\mu=61$, and $\sigma = 11.5$.
Substitute these values into the formula: $z=\frac{84 - 61}{11.5}$.
First, calculate the numerator: $84-61 = 23$.
Then, divide by the standard deviation: $z=\frac{23}{11.5}=2.00$.

Answer:

2.00