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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

Measuring bone density Individuals with low bone density (osteoporosis) have a high risk of broken bones (fractures). Physicians who are concerned about low bone density in patients can refer them for specialized testing. Currently, the most common method for testing bone density is dual-energy X-ray absorptiometry (DEXA). The bone density results for a patient who undergoes a DEXA test usually are reported in grams per square centimeter (g/cm2) and in standardized units. Judy, who is 25years old, has her bone density measured using DEXA. Her results indicate bone density in the hip of 948 g/cm2 and a standardized score of z=鈭�1.45The mean bone density in the hip is 956 g/cm2in the reference population of 25-year-old women like Judy.

a. Judy has not taken a statistics class in a few years. Explain to her in simple language what the standardized score reveals about her bone density.

b. Use the information provided to calculate the standard deviation of bone density in the reference population.

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nMeanSDMinQ1MedQ3Max
5051742.448210.643664146071500095702071836

a. Find and interpret the z-score for North Carolina, with a median household income of $41,553

b. New Jersey had a standardized score of 1.82Find New Jersey鈥檚 median household income for that year.

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following questions.

a. About what percent of bags weigh less than 9.02 ounces? Show your method clearly.

b. A bag that weighs9.07 ounces is at about what percentile in this distribution? Justify your answer.

Teacher raises A school system employs teachers at salaries between \(38,000 and Page Number: 107\)70,000 The teachers鈥� union and school board are negotiating the form of next year鈥檚 increase in the salary schedule. Suppose that every teacher is given a $1000 raise. What effect will these raises have on each of the following characteristics of the resulting distribution of salary?

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