Answer:
Thomas had an ERA with a z-score of -2.82.
Karla had an ERA with a z-score of -2.81.
Thomas had the better year compared with his peers, since his ERA had the lower Zscore.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
The ERA is the Earned Runs Average per 9 innings. This mean that the lower the ERA is, the better it is. So, between Thomas and Karla, whoever has the lower Zscore had the better season.
Thomas
For the males, the mean ERA was 4.837 and the standard deviation was 0.541. This means that .
Thomas ERA was 3.31. This means that
Thomas had an ERA with a z-score of -2.82.
Karla
For Females, the mean ERA was 4.533 and the standard deviation was 0.539. This means that .
Karla ERA was 3.02. So .
Karla had an ERA with a z-score of -2.81
Which player had a better year in comparison with their peers?
Thomas had the better year compared with his peers, since his ERA had the lower Zscore.