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 1.58 . \( 1 \mathbf{2} \) Part 2 of 2 The \( z \)-score corresponding to the youngest senator of age 36 is

To find the \( z \)-score for the youngest senator of age 36, we can use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \( X \) is the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. Given: - \( X = 36 \) (age of the youngest senator) - \( \mu = 63 \) (average age) - \( \sigma = 12 \) (standard deviation) Plugging in the values: \[ z = \frac{(36 - 63)}{12} = \frac{-27}{12} = -2.25 \] So the \( z \)-score corresponding to the youngest senator of age 36 is **-2.25**. This means the youngest senator is 2.25 standard deviations below the average age of their peers in the Senate.