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 1 of 2 The \( z \)-score corresponding to the oldest senator of age 82 is Part: \( \mathbf{1} / \mathbf{2} \) of 2

To calculate the \( z \)-score for the oldest senator who is 82 years old, you use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] Where: - \( X \) = age of the senator (82) - \( \mu \) = mean age (63) - \( \sigma \) = 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 is approximately \( 1.58 \). For the youngest senator, who is 36 years old, you would apply the same formula: \[ z = \frac{(36 - 63)}{12} = \frac{-27}{12} \approx -2.25 \] This means the \( z \)-score corresponding to the youngest senator is approximately \( -2.25 \).