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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鈥攕he scored 30points higher than Gina.

b. Colleen鈥攈er standardized score is higher than Gina鈥檚.

c. Gina鈥攈er standardized score is higher than Colleen鈥檚.

d. Gina鈥攖he standard deviation was larger in 2016

e. The two cousins did equally well鈥攖heir z-scores are the same.

Short Answer

Expert verified

The correct option is (c) Gina鈥攈er standardized score is higher than Colleen鈥檚.

Step by step solution

01

Given information

渭G=470

蟽G=110

xG=500

渭C=510

蟽C=103

xC=530

02

Concept

z=x鈭�渭蟽

03

Calculation

zG=x鈭�渭蟽=500鈭�470110=0.27zC=x鈭�渭蟽=530鈭�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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Most popular questions from this chapter

Put a lid on it! Refer to Exercise 56. The supplier is considering two changes to reduce the percent of its large-cup lids that are too small to less than 1%. One strategy is to adjust the mean diameter of its lids. Another option is to alter the production process, thereby decreasing the standard deviation of the lid diameters.

(a) If the standard deviation remains at 蟽=0.02inches, at what value should the supplier set the mean diameter of its large-cup lids to ensure that less than 1%are too small to fit? Show your method.

(b) If the mean diameter stays at 渭=3.98inches, what value of the standard deviation will result in less than 1%of lids that are too small to fit? Show your method.

(c) Which of the two options in (a) and (b) do you think is preferable? Justify your answer. (Be sure to consider the effect of these changes on the percent of lids that are too large to fit.)

IQ test scores Scores on the Wechsler Adult Intelligence Scale (an IQ test) for the 20- to 34-year-old age group are approximately Normally distributed with 渭=110 and 蟽=25 .

a. What percent of people aged 20 to 34 have IQs between 125 and 150?

b. MENSA is an elite organization that admits as members people who score in the top 2% on IQ tests. What score on the Wechsler Adult Intelligence Scale would an individual aged 20 to 34 have to earn to qualify for MENSA membership?

Standard Normal areas Find the proportion of observations in a standard Normal distribution that satisfies each of the following statements.

a. z<鈭�2.46

b. 0.89<z<2.46

Normal states? The Normal probability plot displays data on the areas (in thousands of square miles) of each of the 50 states. Use the graph to determine if the distribution of land area is approximately Normal.

Jorge鈥檚 score on Exam 1in his statistics class was at the 64thpercentile of the scores for all students. His score falls

a. between the minimum and the first quartile.

b. between the first quartile and the median.

c. between the median and the third quartile.

d. between the third quartile and the maximum.

e. at the mean score for all students.
See all solutions

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