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finalques - Review Questions to Prepare for the Exam 1...

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Review Questions to Prepare for the Exam 1) George Constanza, the character on Seinfeld, is a perpetual loser who keeps trying. As long-time viewers of the show know, only 10% of the women George approaches are willing to go out with him. George often will introduce himself, and then preface his invitation by saying “So waddya doin’ Friday night?” Three quarters of the women who don’t want to go out with him tell him they are busy – “I’m giving my Doberman a bath.” Only one quarter of the women who are willing to go out with him say they are busy. If George finds a woman who admits to being free on Friday night, what is the probability she will go out with him? 2) A random sample is drawn from a population believed to be approximately normally distributed. The sample values are 6, 18, 3, 21, 16, 9, 13, 14, 17 a) From this sample, compute the sample mean, sample median, sample standard deviation. b) Compute a 98% confidence interval for µ . c) If you wanted to verify the claim that the population is approximately normally distributed, what graphical procedure could you use? Explain what would you be looking for. <Hint: While a histogram or dotplot isn't a bad idea, the right answer is a more sophisticated tool.> 3) A student is rushing off to class when she remembers she needs to bring two floppy disks with her. She has 10 disks on her desk, but unfortunately four of them are defective, and she doesn’t know which four. Being in a hurry she grabs three disks at random, figuring that there will probably be two good ones among the three. a) What is the probability that at least two of the three disks are good? b) She has three hours of work to do on the computers at the lab. During the day, network crashes occur randomly and independently at the rate of a crash every 35 hours. What is the probability she will experience exactly one network crash while working in the computer lab? 4) Suppose the GPA’s of prospective Commerce majors at Virginia are normally distributed with a mean of 3.05 and a standard deviation of .31. a) What percentage of prospective Commerce majors have at least a B (that is, 3.0) GPA b) If the Commerce department wanted to pick a minimum GPA to use as a cutoff for admission to their program, and wanted a rule that would eliminate the weakest 35% of its applicants, what minimum GPA would it select?
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5) A couple involved in a long-distance romance speak on the phone once a day, every day. The length of their calls are a random variable with the following distribution (in minutes): 10 .2 20 .3 30 .3 40 .2
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