Review Exercises 119 33. From a random sample of households, the number of televisions are listed. Find the sample mean and the sample standard deviation of the data. Number of televisions 0 1 2 3 4 5 Number of households 1 8 13 10 5 3 34. From a random sample of airplanes, the number of defects found in their fuselages are listed. Find the sample mean and the sample standard deviation of the data. Number of defects 0 1 2 3 4 5 6 Number of airplanes 4 5 2 9 1 3 1 In Exercises 35 and 36, find the coefficient of variation for each of the two data sets. Then compare the results. 35. Sample grade point averages for freshmen and seniors are listed. Freshmen 2.8 1.8 4.0 3.8 2.4 2.0 0.9 3.6 1.8 Seniors 2.3 3.3 1.8 4.0 3.1 2.7 3.9 2.6 2.9 36. The ages and years of experience for all lawyers at a firm are listed. Ages 66 54 47 61 36 59 50 33 Years of experience 37 20 23 32 14 29 22 8 Section 2.5 In Exercises 37– 40, use the data set, which represents the model 2020 vehicles with the highest fuel economies (in miles per gallon) in the most popular classes. (Source: U.S. Environmental Protection Agency) 36 30 30 45 31 113 113 33 33 33 52 141 56 117 58 118 50 26 23 23 27 48 22 22 22 121 41 105 35 35 37. Find the five-number summary of the data set. 38. Find the interquartile range of the data set. 39. Draw a box-and-whisker plot that represents the data set. 40. About how many vehicles fall on or below the third quartile? 41. Find the interquartile range of the data set from Exercise 13. 42. The weights (in pounds) of the defensive players on a high school football team are shown below. Draw a box-and-whisker plot that represents the data set and describe the shape of the distribution. 173 145 205 192 197 227 156 240 172 208 185 190 167 212 228 190 184 195 43. A student’s test grade of 75 represents the 65th percentile of the grades. What percent of students scored higher than 75? 44. As of April 2021, there were 682 top-40 radio stations in the United States. One station finds that 115 stations have a larger daily audience than it has. What percentile does this station come closest to in the daily audience rankings? (Source: Radio-Locator.com) The towing capacities (in pounds) of all the pickup trucks at a dealership have a bell-shaped distribution, with a mean of 11,830 pounds and a standard deviation of 2370 pounds. In Exercises 45– 48, use the corresponding z-score to determine whether the towing capacity is unusual. Explain your reasoning. 45. 16,500 pounds 46. 5500 pounds 47. 18,000 pounds 48. 11,300 pounds
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