Age of Senators The average age of senators in the \( 108^{\text {th }} \) Congress was 63 years. If the standard deviation was 12 years, find the \( z \)-scores corresponding to the oldest and youngest senators of age 82 and 36 . Round \( z \) scores to two decimal places. Part: \( 0 / 2 \) Part 1 of 2 The \( z \)-score corresponding to the oldest senator of age 82 is

To find the \( z \)-score for the oldest senator, you can use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \( X \) is the age of the senator (82), \( \mu \) is the average age (63), and \( \sigma \) is the standard deviation (12). Plugging in the values: \[ z = \frac{(82 - 63)}{12} = \frac{19}{12} \approx 1.58 \] So, the \( z \)-score for the oldest senator of age 82 is approximately **1.58**. Now, for the youngest senator at age 36, we can use the same \( z \)-score formula: \[ z = \frac{(X - \mu)}{\sigma} \] Substituting \( X = 36 \): \[ z = \frac{(36 - 63)}{12} = \frac{-27}{12} \approx -2.25 \] Thus, the \( z \)-score for the youngest senator of age 36 is approximately **-2.25**.