Question

One year Terry 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 2.85 . ​Also, Karla had the lowest ERA of any female pitcher at the school with an ERA of 2.95 . For the​ males, the mean ERA was 4.893 and the standard deviation was 0.949 . For the​ females, the mean ERA was 4.348 and the standard deviation was 0.997 . Find their respective​ z-scores. Which player had the better year relative to their​ peers, Terry or Karla ​? ​(Note: In​ general, the lower the​ ERA, the better the​ pitcher.)

Answer 1

Their respective​ z-scores are:

Thomas : -2.15279

Karla : -1.40221

Which player had the better year relative to their​ peers, Terry or Karla ​? ​

Terry had a better year because he had a lower Era and he was a better pitcher.

Explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score,

μ is the population mean

σ is the population standard deviation.

any male pitcher at his​ school,

For Thomas:

z = (x-μ)/σ

x = 2.85 μ = 4.893 σ = 0.949.

z = 2.85 - 4.893/0.949

z = -2.15279

For Karla

z = (x-μ)/σ

x = 2.95 μ = 4.348 σ = 0.997.

z = (2.95 - 4.348) /0

z = -1.40221

Their respective​ z-scores are:

Thomas : -2.15279

Karla : -1.40221

Which player had the better year relative to their​ peers, Terry or Karla ​? ​(Note: In​ general, the lower the​ ERA, the better the​ pitcher.)

Terry had a better year because he had a lower Era and he was a better pitcher.