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Chapter 2: Q 19. (page 106)

SAT versus ACT Eleanor scores 680 on the SAT Mathematics test. The distribution of SAT Math scores is symmetric and single-peaked with mean 500 and a standard deviation 100 Gerald takes the American College Testing (ACT) Mathematics test and scores 29ACT scores also follow asymmetric, single-peaked distribution—but with mean 21 and standard deviation of 5 Find the standardized scores for both students. Assuming that both tests measure the same kind of ability, who has the higher score?

Short Answer

Expert verified

Eleanor =1.8

Gerald =1.6

Step by step solution

01

Given information

SAT score:

Eleanor score=680

Mean =500

Standard deviation =100

ACT score:

Gerald score =29

Mean =21

Standard deviation =5

02

Concept

The formula used: z=x−μσ

03

Calculation

Standardized score:

ForEleanor:ForGerald:z=680−500100z=29−215z=1.8z=1.6

Eleanor's z-score is greater than Gerald's, hence Eleanor's score is larger than Gerald's.

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