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

Question

One year Josh 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 3.44. Also, Nina had the lowest ERA of any female pitcher at the school with an ERA of 3.26. For the males, the mean ERA was 4.742 and the standard deviation was 0.724. For the females, the mean ERA was 3.971 and the standard deviation was 0.981. Find their respective z-scores. Which player had the better year relative to their peers, Josh or Nina? (Note: In general, the lower the ERA, the better the pitcher.) Josh had an ERA with a z-score of nothing. Nina had an ERA with a z-score of nothing. (Round to two decimal places as needed.) Which player had a better year in comparison with their peers? A. Nina had a better year because of a lower z-score. B. Josh had a better year because of a higher z-score. C. Josh had a better year because of a lower z-score. D. Nina had a better year because of a higher z-score. Click to select your answer(s).

Explanation / Answer

Josh's z-score = (X - mean)/sd

                        = (3.44 - 4.742)/0.724

                        = -1.80

Nina's z-score = (X - mean)/sd

                        = (3.26 - 3.971)/0.981

                        = -0.72

Option - D) Naina had a better year because of a higher z-score.

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