302 CHAPTER 6 Normal Probability Distributions Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped. 9. M&Ms The weights (grams) of the red M&M plain candies, as listed in Data Set 38 “Candies” in Appendix B 10.Taxi Trips The distances (miles) traveled by New York City taxis transporting customers, as listed in Data Set 32 “Taxis” in Appendix B 11.Small World The waiting times (minutes) for the Disney World ride Small World at 5:00 PM, as listed in Data Set 33 “Disney World Wait Times” in Appendix B 12.Dunkin’ Donuts The drive-through service times (seconds) of Dunkin’ Donuts lunch customers, as listed in Data Set 36 “Fast Food” in Appendix B Using Technology to Generate Normal Quantile Plots. In Exercises 13–16, use the data from the indicated exercise in this section. Use software (such as Statdisk, Minitab, Excel, or StatCrunch) or a TI-83, 84 Plus calculator to generate a normal quantile plot. Then determine whether the data come from a normally distributed population. 13. Exercise 9 “M&Ms” 14. Exercise 10 “Taxi Trips” 15. Exercise 11 “Small World” 16. Exercise 12 “Dunkin’ Donuts” Constructing Normal Quantile Plots. In Exercises 17–20, use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. Construct the normal quantile plot, then determine whether the data appear to be from a population with a normal distribution. 17.Body Temperatures A sample of body temperatures 1°F2 of women from Data Set 5 “Body Temperatures” in Appendix B: 98.7, 98.4, 98.0, 97.9, 98.2 18.Earthquake Depths A sample of depths (km) of earthquakes is obtained from Data Set 24 “Earthquakes” in Appendix B: 17.3, 7.0, 7.0, 7.0, 8.1, 6.8. 19. Brain Volumes A sample of human brain volumes 1cm32 is obtained from those listed in Data Set 12 “IQ and Brain Size” in Appendix B: 1027, 1029, 1034, 1070, 1079, 1079, 963, 1439. 20. Ages of Oscar-Winning Actresses A sample of the ages (years) of actresses who won Oscars, as listed in Data Set 21 “Oscar Winner Age” in Appendix B: 25, 24, 41, 30, 27, 35, 33, 29, 80 21. Transformations The heights (in inches) of women listed in Data Set 1 “Body Data” in Appendix B have a distribution that is approximately normal, so it appears that those heights are from a normally distributed population. a. If 2 inches is added to each height, are the new heights also normally distributed? b. If each height is converted from inches to centimeters, are the heights in centimeters also normally distributed? c. Are the logarithms of the normally distributed heights also normally distributed? 22.Lognormal Distribution The following are the values of net worth (in millions of dollars) of recent members of the executive branch of the U.S. government. Test these values for normality, then take the logarithm of each value and test for normality. What do you conclude? 1297 15.8 7.08 1.05 0.73 0.08 0.23 0.19 6-5 Beyond the Basics
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