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Chapter 2: Q 36. (page 108)

George’s average bowling score is180; he bowls in a league where the average for all bowlers is 150 and the standard deviation is 20Bill’s 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’s 180

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

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’s.

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’s.

Step by step solution

01

Given information

For 1st bowler

x=180,μ=150,σ=20

For 2nd bowler

x=190,μ=160,σ=15

02

Concept

The formula used: Z=x−μσ

03

Calculation

Formula for z-score

Z=x−μσZGeorge=180−15020=1.5ZBill=190-16015=2ZBill>ZGeorge

So the correct choice is (b).

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