774 APPENDIX D Section 3-3 1. Brady’s height is 2.66 standard deviations above the mean. 3. It appears that weights of U.S. Army males increased from 1988 to 2012. 5. a. 27.8 mm Hg b. 2.48 standard deviations c. z = 2.48 d. The diastolic blood pressure of 98 mm Hg is significantly high. 7. a. 52.4 minutes b. 2.00 standard deviations c. z = 2.00 d. The commute time of 95.0 minutes is significantly high because z Ú 2.0. 9. Significantly low values are less than or equal to 10.7; significantly high values are greater than or equal to 31.5; values that are not significant are between 10.7 and 31.5. 11. Significantly low values are less than or equal to 19.0 in.; significantly high values are greater than or equal to 23.8 in.; values that are not significant are between 19.0 in. and 23.8 in. 13. With z scores of 13.79 and –16.83, the z score of –16.83 is farther from the mean, so Chandra Bahadur Dangi has a height that is more extreme. 15. Male: z score = -2.69; female: z score = -2.18. The male has the more extreme weight. 17. 6th percentile 19. 40th percentile 21. 0.95 W>kg (Tech: Minitab: 0.942 W>kg; Excel: 0.958 W>kg) 23. 1.28 W>kg (Tech: Minitab: 1.285 W>kg) 25. 1.155 W>kg 27. 0.91 W>kg 29. 5-number summary: 2, 6.0, 7.0, 8.0, 10. 31. 5-number summary: 128 mBq, 140.0 mBq, 150.0 mBq, 158.5 mBq, 172 mBq (Tech: Minitab yields Q1 =139.0 mBq and Q3 = 159.75 mBq. Excel yields Q1 = 141.0 mBq and Q3 = 157.25 mBq.) 33. The top boxplot represents males. Males appear to have slightly lower pulse rates than females. (Tech: For males, Minitab yields Q3 = 77.) 35. The top boxplot represents the weights from ANSUR I 1988 and the bottom boxplot represents weights from ANSUR II 2012. It appears that the weights of male Army personnel increased somewhat from 1988 to 2012. (Tech: For ANSUR II 2012, Minitab yields Q1 = 75.575 and Q3 = 94.425. TI data: The values of the five-number summary for ANSUR I are 11. Range = $150.0; s2 = 2513.9 dollars2; s = $50.1. These statistics are measuring variation among the sample of prices. The minimum price would be a particularly helpful statistic, but none of these statistics is helpful for selecting a smart thermostat for purchase. 13. Range = 55.0 mg; s2 = 413.4 mg2; s = 20.3 mg. Americans consume some brands much more often than others, but the 20 brands are all weighted equally in the calculations, so the statistics are not necessarily representative of the population of all cans of the same 20 brands consumed by Americans. 15. Range = 1.0; s2 = 0.2; s = 0.4. Because the numbers are replacements for “right” and “left,” they are at the nominal level of measurement, and the results are meaningless. 17. Range = $2461.0; s2 = 290,400.4 1dollars22; s = $538.9. The amounts of $1500 and $2500 appear to be outliers, and it is likely that they have a large effect on the measures of variation. 19. Range = 50.0 cigarettes; s2 = 89.7 cigarettes2; s = 9.5 cigarettes. Because the selected subjects report the number of cigarettes smoked, it is very possible that the data are not at all accurate, so the results might not reflect the actual smoking behavior of California adults. 21. Systolic: 14.6%. Diastolic: 16.9%. The variation is roughly about the same. 23. Males: 16.2%. Females: 11.2%. Pulse rates of males appear to vary more than pulse rates of females. 25. Range = 3.10°F; s2 = 0.391°F22; s = 0.62°F 27. Right Threshold: Range = 70.0; s2 = 160.7; s = 12.7. Left Threshold: Range = 75.0; s2 = 164.9; s = 12.8. Amounts of variation for the left and right thresholds do not appear to be very different. 29. 0.78°F, which is not substantially different from s = 0.62°F found using all of the data. 31. Right Threshold: 17.5, which is reasonably close to s = 12.7 found using all of the data. Left Threshold: 18.8, which is in the ballpark of 12.8 found using all of the data. 33. Significantly low values are less than or equal to 41.4 years, and significantly high values are greater than or equal to 69.0 years. An age of 35 years would be significantly low. 35. Significantly low values are less than or equal to 24.74 cm, and significantly high values are greater than or equal to 29.90 cm. A foot length of 30 cm is significantly high. 37. s = 20.4 minutes is very close to the exact value of 18.5 minutes. 39. s = 7.1 years is very close to the exact value of 6.9 years. 41. a. 95% b. 68% 43. At least 89% of women have platelet counts within 3 standard deviations of the mean. The minimum is 58.9 and the maximum is 451.3. 45. a. 24.7 cigarettes2 b. 24.7 cigarettes2 c. 12.3 cigarettes2 d. Part (b), because repeated samples result in variances that target the same value 124.7 cigarettes22 as the population variance. Use division by n - 1. e. No. The mean of the sample variances 124.7 cigarettes22 equals the population variance 124.7 cigarettes22, but the mean of the sample standard deviations (3.5 cigarettes) does not equal the population standard deviation (5.0 cigarettes).
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