One year Larry 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 2.98. Also, Vanessa had the lowest ERA of any female pitcher at the school with an ERA of 3.44. For the males, the mean ERA was 4.221 and the standard deviation was 0.898. For the females, the mean ERA was 5.325 and the standard deviation was 0.799. Find their respective z-scores. Which player had the better year relative to their peers, Larry or Vanessa? (Note: In general, the lower the ERA, the better the pitcher.)
To determine which player had a better year relative to their peers, compute each player's z-score. The population z-score can be found using the formula below, where x is the player's ERA, mu is the appropriate population mean and sigma is the appropriate population standard deviation.