One year
HankHank
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
3.293.29.
Also,
KarenKaren
had the lowest ERA of any female pitcher at the school with an ERA of
2.992.99.
For the males, the mean ERA was
4.4024.402
and the standard deviation was
0.6370.637.
For the females, the mean ERA was
4.7524.752
and the standard deviation was
0.8070.807.
Find their respective z-scores. Which player had the better year relative to their peers,
HankHank
or
KarenKaren?
(Note: In general, the lower the ERA, the better the pitcher.)
Hank
Hank had an ERA with a z-score of ---?
karen had an ERA with a z-score of---?
Answer)
Z = (x-mean)/s.d
For males
Mean = 4.402
S.d = 0.637
Hank's score = 3.29
Z = (3.29 - 4.402)/0.637
Z = -1.75
For females
Mean = 4.752
S.d = 0.807
and karen's score is 2.99
Z = (2.99 - 4.752)/0.807
Z = -2.18
So, karen had the better year due to lower z score
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