One year Sam had the lowest ERA (earned-run average, mean number of runs yielded
ID: 2946275 • Letter: O
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 2.92. Also, Karen had the lowest ERA of any female pitcher at the school with an ERA of 3.35. For the males, the mean ERA was 4.157 and the standard deviation was 0.946. For the females, the mean ERA was 4.934 and the standard deviation was 0.938. Find their respective z-scores. Which player had the better year relative to their peers, Sam or Karen? (Note: In general, the lower the ERA, the better the pitcher.) Sam had an ERA with a z-score of Karen had an ERA with a z-score of Round to two decimal places as needed.)Explanation / Answer
z-score = X - Mean / Standard deviation
For Sam,
z-score = 2.92 - 4.157 / 0.946
= -1.31
Sam had an ERA with a z-score of -1.31
For karen,
z-score = 3.35 - 4.934 / 0.938
= -1.69
Karen had an ERA with the z-score of -1.69
Since Saren has lower z-score , Saren had better year.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.