Question

One year

HankHank

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

3.293.29.

​Also,

KarenKaren

had the lowest ERA of any female pitcher at the school with an ERA of

2.992.99.

For the​ males, the mean ERA was

4.4024.402

and the standard deviation was

0.6370.637.

For the​ females, the mean ERA was

4.7524.752

and the standard deviation was

0.8070.807.

Find their respective​ z-scores. Which player had the better year relative to their​ peers,

HankHank

or

KarenKaren​?

​(Note: In​ general, the lower the​ ERA, the better the​ pitcher.)

Hank

Hank had an ERA with a​ z-score of ---?

karen had an ERA with a​ z-score of---?

Answer 1

Answer)

Z = (x-mean)/s.d

For males

Mean = 4.402

S.d = 0.637

Hank's score = 3.29

Z = (3.29 - 4.402)/0.637

Z = -1.75

For females

Mean = 4.752

S.d = 0.807

and karen's score is 2.99

Z = (2.99 - 4.752)/0.807

Z = -2.18

So, karen had the better year due to lower z score