Question

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 2.59. ​Also, Beth had the lowest ERA of any female pitcher at the school with an ERA of 2.66. For the​ males, the mean ERA was 3.986 and the standard deviation was 0.541. For the​ females, the mean ERA was 4.068 and the standard deviation was 0.806. Find their respective​ z-scores. Which player had the better year relative to their​ peers, Sam or Beth​? ​(Note: In​ general, the lower the​ ERA, the better the​ pitcher.)

Answer 1