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

z score Perry
`z=-1.402`

z score Alice
`z=-1.722`

Alice had better year in comparison with Perry.

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=(x-\mu)/(\sigma)`

Here μ=4.206 and σ=0.846

`z=(3.02-4.206)/(0.846)`

`z=(-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=(3.16-4.519 )/(0.789)`

`z=(-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.