Answer:
Kershaw had the lower Z-score, this means that he had the better year.
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 Kershaw and Hernandez, whoever has the lower Zscore had the better season.
Kershaw
ERA of 1.77, so
.
In the National League, the mean ERA in 2014 was 3.430 and the standard deviation was 0.721. This means that
. So:



Hernandez
ERA of 2.14, so
.
In the American League, the mean ERA in 2014 was 3.598 and the standard deviation was 0.762. This means that
.



Kershaw had the lower Z-score, this means that he had the better year.