4.9 One year Hank had the lowest ERA (eaned-run average, mean number of runs yie

Question

4.9 One year Hank had the lowest ERA (eaned-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, Betty had the lowest ERA of any female pitcher at the school with an ERA of 2.74. For the males, the mean ERA was 3.719 and the standard deviation was 0 503. For the females, the mean ERA was 3.894 and the standard deviation was 0.995. Find their respective z-scores. Which player had the better year relative to their peers, Hank or Betty? (Note: In general, the lower the ERA, the better the pitcher) Hank had an ERA with a z-score of Betty had an ERA with a z-score of (Round to two decimal places as needed.)

Explanation / Answer

z= (X -mean)/sd
z-score for Hank = (3.12 - 3.719)/0.503 = -1.1908
z-score for Betty = (2.74 - 3.894)/0.995 = -1.15979

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