Respuesta :
Answer:
Thomas had the better year relative to their peers.
Step-by-step explanation:
The complete question is: One year Thomas 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 3.31. Also, Karla had the lowest ERA of any female pitcher at the school with an ERA of 3.02. For the males, the mean ERA was 4.837 and the standard deviation was 0.541. For the females, the mean ERA was 4.533 and the standard deviation was 0.539. Find their respective z-scores. Which player had the better year relative to their peers, or ? (Note: In general, the lower the ERA, the better the pitcher.)
We are given that for the males, the mean ERA was 4.837 and the standard deviation was 0.541. For the females, the mean ERA was 4.533 and the standard deviation was 0.539.
As, we know that the z-score is calculated by the following formula;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean
[tex]\sigma[/tex] = standard deviation
Now, firstly we will calculate the z score for Thomas;
z-score = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{3.31-4.837}{0.541}[/tex] = -2.823
{Here, the mean ERA for the males was 4.837 and the standard deviation was 0.541}
Similarly, we will calculate the z score for Karla;
z-score = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{3.02-4.533}{0.539}[/tex] = -2.807
{Here, the mean ERA for the females was 4.533 and the standard deviation was 0.539}
Now, it is stated in the question that the lower the ERA, the better the pitcher.
So, we can clearly see that Thomas had a lower ERA of z-score as -2.823 < -2.807. This means that Thomas had the better year relative to their peers.
