George has an average bowling score of 180 and bowls in a league where the average for all bowlers is 150 and the standard deviation is 20. Bill has an average bowling score of 190 and bowls in a league where the average is 160 and the standard deviation is 15. Who ranks higher in his own league, George or Bill?
A) Bill because his 190 is higher than George's 180.
B) Bill because his standard score is higher than George's.
C) George because his standard score is higher than Bill's.
D) Bill and George have the same rank in their leagues because both are 30 pins above the mean.

Question

Quizplus · Accepted Answer

To compare the performance of two bowlers from different leagues, we need to use the concept of standard scores (also called z-scores).

Bill's standard score = (190 - 160) / 15 = 2.

This means that Bill's average score is two standard deviations above the mean score in his own league.

George's standard score = (180 - 150) / 20 = 1.5.

This means that George's average score is 1.5 standard deviations above the mean score in his own league.

Therefore, Bill ranks higher in his own league because his standard score is higher than George's.

George Has an Average Bowling Score of 180 and Bowls