Question

One year Rodger had the lowest ERA (earned-run average, mean number of runs yielded per nin innings pitched) of any male pitcher at his school, with an ERA of 2.67. Also, Betty had the lowest ERA of any female pitcher at the school with an ERA of 3.273 For the males, the mean ERA was 4.408 and the standard deviation was 0.694. For the females, the mean ERA was 4.017 and the standard deviation was 0.533. Find their respective z-scores. Which player had the better year relative to their peers, Roger or Betty? (Note: In general, the lower the ERA, the better the pitcher).

Roger had an ERA with a z-score of ___

Betty 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?

Answer 1

For the males, the mean ERA was 4.408 and the standard deviation was 0.694 and Rodger has an ERA of 2.67

so, we get mean = 4.408, sigma = 0.694 and x = 2.67

z = (x-mean)/sigma

= (2.67-4.408)/0.694

= -2.50

For the females, the mean ERA was 4.017 and the standard deviation was 0.533 and Betty has an ERA of 3.273

so, we get mean = 4.017, sigma = 0.533 and x = 3.273

z = (x-mean)/sigma

= (3.273-4.017)/0.533

= -1.40

It is clear that Betty has a large z score as compared to Rodger, so we can say that Betty had a better year.