One year Terry had the lowest ERA (earned-run average, mean number of runs yield

Question

One year Terry 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 2.67. .Also, Beth had the lowest ERA of any female pitcher at the school with an ERA of 3.28. For the males, the mean ERA was 4.405 and the standard deviation was 0.739. For the females, the mean ERA was 4.281 and the standard deviation was 0.672. Find their respective z-scores. Which player had the better year relative to their peers, Terry or Beth?

Explanation / Answer

Terry had an ERA with a z score of z1=(x-)/

=(2.67-4.405)/0.739

=-2.34

Beth had an ERA with a z score of z2=(x-)/

=(3.28-4.281)/0.672

=-1.48

Thus, Beth has a relatively higher z score.

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