3.4.9 Question Help * One year Mike had the lowest ERA (eamed-run average, mean

Question

3.4.9 Question Help * One year Mike had the lowest ERA (eamed-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.37. Also, Jane had the lowest ERA of any female pitcher at the school with an ERA of 2.98 For the males, the mean ERA was 3.805 and the standard deviation was 0.655. For the females, the mean ERA was 4.285 and the standard deviation was 0.584. Find their respective z-scores. Which player had the better year relative to their peers, Mike or Jane? (Note: In general, the lower the ERA, the better the pitcher) Mike had an ERA with a z-score of Jane had an ERA with a z-score of (Round to two decimal places as needed)

Explanation / Answer

Solution:

Mike had an ERA with a Z-score of  
Z = x - / = 3.37 - 3.805/0.655
= -0.6641
Jane has an ERA with a Z - score of
Z = x - / = 2.98 - 4.285/0.584
= -2.2345

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