This Question: 1 pt 4 8 of 12 (6 This Test: 12 pts One year Todd had the lowest

Question

This Question: 1 pt 4 8 of 12 (6 This Test: 12 pts One year Todd had the lowest ERA (eamed-run average mean number of runs yiekded per nine innings pitched) of any male pitcher at hes schoo wth an ERA of 2 79 Also, Susan had the lowest ERA of any temale ptcher at the school with an ERA o13 23. For the males, the mean ERA was 3 857 and the standard deviation was 0 945 For the temakes, the mean ERA was 3 865 and the standard deviation was 0 877 Find her respective z-scores. Which player had the better year relative to their peers, Tood or Susan? (Note: in general, the lower the ERA, the better the pitcher ) Todd had an ERA with a z-score of Susan had an ERA with a z-score of Round to two decimal places as needed ) Which player had a better year in comparison with their peers? O A. Tood had a better year because of a lower z-score O B. Todd had a beter year because of a higher 2 score O c. Susan had a better year because of a higher z -score O D. Susan had a better year because of a lower 2-score

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)

MALE DATA
mean ( u ) = 3.857
standard Deviation ( sd )= 0.945
P(X = 2.79) = (2.79-3.857)/0.945
= -1.067/0.945
Z VALUE = -1.1291

FEMALE DATA
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 3.865
standard Deviation ( sd )= 0.877
P(X < 3.23) = (3.23-3.865)/0.877
= -0.635/0.877
Z VALUE = -0.7241

b.
Tood had a better year because of lower z-score

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