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Chapter 2: Q T2.10. (page 149)

Until the scale was changed in 1995SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the early 1990swas 470and the standard deviation was 110 In 2016 the mean was 510and the standard deviation was 103 Gina took the SAT in 1994and scored 500Her cousin Colleen took the SAT in 2016 and scored 530 Who did better on the exam, and how can you tell?

a. Colleen—she scored 30points higher than Gina.

b. Colleen—her standardized score is higher than Gina’s.

c. Gina—her standardized score is higher than Colleen’s.

d. Gina—the standard deviation was larger in 2016

e. The two cousins did equally well—their z-scores are the same.

Short Answer

Expert verified

The correct option is (c) Gina—her standardized score is higher than Colleen’s.

Step by step solution

01

Given information

μG=470

σG=110

xG=500

μC=510

σC=103

xC=530

02

Concept

z=x−μσ

03

Calculation

zG=x−μσ=500−470110=0.27zC=x−μσ=530−510103=0.19

It has been discovered that zG>zC implying that the person with the greatest z-score will perform higher on SAT exam in comparison to the year in which they took the exam.

Hence, the correct option is (c)

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