# 8 in a large population of college students 20 of the

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8.In a large population of college students, 20% of the students have experienced feelings ofmath anxiety.If you take a random sample of 10 students from this population, the meanand standard deviation of the number of students in the sample who have experienced mathanxiety is:(a)P= 1.6;V= 1.414(b)P= 1.6;V= 1.265(c)P= 2;V= 1.6(d)P= 2;V= 1.414(e)P= 2;V= 1.265
¶ºWhich of the following is a true statement?.
© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 6277
278The Practice of Statistics, 4/e- Chapter 6© 2011 BFW PublishersPart 2:Free ResponseShow all your work.Indicate clearly the methods you use, because you will be graded on thecorrectness of your methods as well as on the accuracy and completeness of your results andexplanations.10.A company that rents DVDs from vending machines in grocery stores has developed thefollowing probability distribution for the random variableX= the number of DVDs acustomer rents per visit to a machine.(a)Find and interpret the mean (expected value) ofX(b) Find and interpret the standard deviation ofX(c)Suppose the profit the company makes on each customer visit is \$0.75 per DVD minus\$0.05 “fixed costs.”That is, ifP= profit, then0.750.05.PXµUse a lineartransformation of your results in (a) and (b) to find the mean and standard deviation forP.X12P(X)0.50.30.1..340.1
© 2011 BFW PublishersThe Practice of Statistics, 4/e- Chapter 627911.ACT scores for the 1,171,460 members of the 2004 high school graduating class who tookthe test closely followed the Normal distribution with mean 20.9 and standard deviation 4.8.Choose two students independently and at random from this group.(a) What is the expected difference in their scores?(b) What is the standard deviation of the difference in their scores?(c) Find the probability that the difference in the two students’ scores is greater than 6.12.A professional soccer player succeeds in scoring a goal on 84% of his penalty kicks.Assumethat the success of each kick is independent.(a) In a series of games, what is the probability that the first time he failsto score a goal is onhis fifth penalty kick?(b) What is the probability that he scores on 5 or fewer of his next 10 penalty kicks?

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