3.4.9 Question Help One year Sam had the lowest ERA (earned-run average, mean nu

Question

3.4.9 Question Help One year Sam 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 2.97. Also, Betty had the lowest ERA of any female pitcher at the school with an ERA of 2.64 For the males, the mean ERA was 4.579 and the standard deviation was 0.664. For the females, the mean ERA was 4.908 and the standard deviation was 0.813. Find their respective z-scores. Which player had the better year relative to their peers, Sam or Betty? (Note: In general, the lower the ERA, the better the pitcher.) a. Sam 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

here as we know that z score =(X-mean)/std deviaiton

SAM had an ERA with z score of =(2.97-4.579)/0.664=-2.42

batty had an ERA with z score of =(2.64-4.908)/0.813=-2.79

from above as Betty has lowest z score therefore she has better year relative to their peers

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