Question

One year, Chris had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.49. Julie had the lowest ERA of any female pitcher at the school with an ERA of 2.75. For the males, the mean ERA was 3.978, and the standard deviation was 0.594. For the females, the mean ERA was 3.856, and the standard deviation was 0.816. Find their respective z-scores. Which player had the better year relative to their peers, Chris or Julie? (Note: In general, the lower the ERA, the better the pitcher.) Chris had an ERA with a z-score of ______.

a) -0.65
b) 1.39
c) -1.22
d) 0.65

Answer 1

Chris had a z-score of -0.808 and Julie had a z-score of -1.361. Based on the z-scores, Chris had a better year relative to his peers compared to Julie.

Step-by-step explanation:

To find the z-score for Chris and Julie, we can use the formula:

z = (x - μ) / σ

For Chris:

z = (3.49 - 3.978) / 0.594 = -0.808

For Julie:

z = (2.75 - 3.856) / 0.816 = - 1.361

Therefore, Chris had a z-score of -0.808 and Julie had a z-score of -1.361.

Based on the z-scores, the closer a z-score is to 0, the better the performance relative to the mean. Since Chris had a z-score closer to 0 (-0.808), he had a better year relative to his peers compared to Julie (-1.361).