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© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 259Chapter 2: Exploring DataContentsExtra Practice I: Measuring location and Normal distributionsExtra Practice II: Measuring location and Normal distributionsStudents often have difficulty the first time they encounter the Normal distribution.These two worksheets provide extra practice usingz-scores and performing calculationswith Normal distributions.Quizzes, Tests, and Solutions
60The Practice of Statistics, 4/e- Chapter 2© 2011 BFW PublishersExtra Practice I: Measuring location and Normal distributionsACT versus SAT, IThere are two major tests of readiness for college, the ACT and the SAT.ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent yearshas been roughly Normal with meanP= 20.9and standard deviationV= 4.8. SAT scores(prior to 2005) were reported on a scale from 400 to 1600. SAT scores have been roughlyNormal with meanP= 1026and standard deviationV= 209.The following exercises arebased on this information.1.Jose scores 1287 on the SAT. Assuming that both tests measure the same thing, what score onthe ACT is equivalent to Jose's SAT score?Explain.2.Reports on a student's ACT or SAT usually give the percentile as well as the actual score.Tonya scores 1318 on the SAT. What is her percentile?Show your method.3.The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75.What are the quartiles of the distribution of ACT scores?Show your method.
© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 261Extra Practice II: Measuring location and Normal distributionsACT versus SAT, IIThere are two major tests of readiness for college, the ACT and the SAT.ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent yearshas been roughly Normal with meanP= 20.9and standard deviationV= 4.8. SAT scores(prior to 2005) were reported on a scale from 400 to 1600. SAT scores have been roughlyNormal with meanP= 1026and standard deviationV= 209.The following exercises arebased on this information.1.Maria scores 28 on the ACT. Assuming that both tests measure the same thing, what score onthe SAT is equivalent to Maria's ACT score?Explain.2.Reports on a student's ACT or SAT usually give the percentile as well as the actual score.Jacob scores 16 on the ACT. What is his percentile?Show your method.3.The quintiles of any distribution are the values with cumulative proportions 0.20, 0.40, 0.60,and 0.80. What are the quintiles of the distribution of SAT scores?Show your method.
62The Practice of Statistics, 4/e- Chapter 2© 2011 BFW PublishersAnswers to Extra PracticeExtra Practice I:1.On the SAT, Jose’sz-score isz=12871026209±= 1.25.To find his equivalent score on theACT, we solve20.91.254.8x±forxand getx= 26.9.

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