Question

One year Perry 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 3.02. ​Also, Alice had the lowest ERA of any female pitcher at the school with an ERA of 3.16. For the​ males, the mean ERA was 4.206 and the standard deviation was 0.846. For the​ females, the mean ERA was 4.519 and the standard deviation was 0.789. Find their respective​ z-scores. Which player had the better year relative to their​ peers, Perry or Alice​

Answer 1

Answer:

z score Perry $z=-1.402$

z score Alice $z=-1.722$

Alice had better year in comparison with Perry.

Step-by-step explanation:

Consider the provided information.

One year Perry had the lowest ERA​ of any male pitcher at his​ school, with an ERA of 3.02. For the​ males, the mean ERA was 4.206 and the standard deviation was 0.846.

To find z score use the formula.

$z=\frac{x-\mu}{\sigma}$

Here μ=4.206 and σ=0.846

$z=\frac{3.02-4.206}{0.846}$

$z=\frac{-1.186}{0.846}$

$z=-1.402$

Alice had the lowest ERA of any female pitcher at the school with an ERA of 3.16. For the​ females, the mean ERA was 4.519 and the standard deviation was 0.789.

Find the z score

where μ=4.519 and σ=0.789

$z=\frac{3.16-4.519 }{0.789}$

$z=\frac{-1.359}{0.789}$

$z=-1.722$

The Perry had an ERA with a z-score is –1.402. The Alice had an ERA with a z-score is –1.722.

It is clear that the z-score value for Perry is greater than the z-score value for Alice. This indicates that Alice had better year in comparison with Perry.