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    Normal Distributions and the Empirical Rule

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    To Satisfy concerns of potential advertisers, the management of OurCampus! has undertaken a research project to learn the amount of time it takes users to download a complex video features page. The marketing department has collected data and has made some claims based on the assertion that the data follow a normal distribution.

    Using a Web browser, open to the Web page for the Chapter 6 Web Case or Open Our_DownloadResearch.htm, if you have downloaded the Web Case files, and read the internal marketing report that reviews these data and conclusions. Then answer the following :

    1. Can the collected data be approximated by the normal distribution?
    2. Review and evaluate the conclusions made by the OurCampus! marketing department. Which conclusions are correct? Which ones are incorrect?
    3. If OurCampus! could improve the mean time by five seconds, how would the probabilities changes?

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    Solution Preview

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    1. Yes, the collected data can be approximated by a normal distribution. To see this, we draw a histogram of the collected data (rounding to the nearest second) and note that it has a clear bell shape. Furthermore, we test some important properties of a normal distribution: that about 68% of observations lie within one standard deviation of the mean (in our case 73%) and that about 95% of observations lie within two standard deviations of the mean (in our case 94%).

    2. It is true that a 15-second download is less likely than a 14 or 13-second download. Even though in our collected data, there were more 15-second downloads than 13- or ...