3.4.9 Question Help One year Chris had the lowest ERA (earned-run average, mean

Question

3.4.9 Question Help 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 3.12. Also, Beth had the lowest ERA of any female pitcher at the school with an ERA of 3.18. For the males, the mean ERA was 4.236 and the standard deviation was 0.952. For the females, the mean ERA was 3.786 and the standard deviation was 0.627. Find their respective z-scores. Which player had the better year relative to their peers, Chris or Beth? (Note: In general, the lower the ERA, the better the pitcher) Chiris or Chris had an ERA with a z-score of Beth had an ERA with a z-score of (Round to two decimal places as needed.)

Explanation / Answer

For Chris, mean is 4.236 and s is 0.952, thus the z score is (x-mean)/s= (3.12-4.236)/0.952=-1.17

For Beth the z score is (3.18-3.786)/0.627=-0.97

thus, Chris has lower ERA

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