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

Question

One year Dan 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 2.93. Also, Susan had the lowest ERA of any female pitcher at the school with an ERA of 2.53. For the males, the mean ERA was 4.109 and the standard deviation was 0.543. For the females, the mean ERA was 3.911 and the standard deviation was 0.869. Find their respective z-scores. Which player had the beter year relative to their peers, Dan or Susan? (Note: In general, the lower the ERA, the better the pitcher.) Dan had an ERA with a z-score of Susan had an ERA with a z-score of (Round to two decimal places as needed.) Which player had a better year in comparison with their peers? O A. O B. Susan had a better year because of a higher z-score. Susan had a better year because of a lower z-score. C. O D. Dan had a better year because of a higher z-score. Dan had a better year because of a lower z-score.

Explanation / Answer

Dan

x = 2.93

mean = 4.109

standard deviation = 0.543

z = (x- mean)/standard deviation = (2.93 - 4.109)/0.543 = - 2.17127 =-2.17

Susan

X = 2.53

mean = 3.911

standard deviation = 0.869

z = (2.53-3.911)/0.869 = -1.58918 =-1.59

Susan had a better year because of lower z score

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