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Chapter 2: Q 36. (page 108)

George鈥檚 average bowling score is180; he bowls in a league where the average for all bowlers is 150 and the standard deviation is 20Bill鈥檚 average bowling score is 190; he bowls in a league where the average is 160and the standard deviation is 15. Who ranks higher in his own league, George or Bill?

a. Bill, because his 190is higher than George鈥檚 180

b. Bill, because his standardized score is higher than George鈥檚.

c. Bill and George have the same rank in their leagues because both are 30pins above the mean.

d. George, because his standardized score is higher than Bill鈥檚.

e. George, because the standard deviation of bowling scores is higher in his league.

Short Answer

Expert verified

The correct option is (b) Bill, because his standardized score is higher than George鈥檚.

Step by step solution

01

Given information

For 1st bowler

x=180,渭=150,蟽=20

For 2nd bowler

x=190,渭=160,蟽=15

02

Concept

The formula used: Z=x鈭�渭蟽

03

Calculation

Formula for z-score

Z=x鈭�渭蟽ZGeorge=180鈭�15020=1.5ZBill=190-16015=2ZBill>ZGeorge

So the correct choice is (b).

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