12.5 The Normal Curve 819 31. To the left of = − z 2.19 0.0143 32. To the right of = − z 1.72 0.9573 33. To the right of = − z 2.25 0.9878 34. To the right of = z 0.62 0.2676 35. Between = − z 1.64 and = − z 1.32 0.0429 36. Between = z 1.23 and = z 1.81 0.0742 In Exercises 37– 46, use Table 12.8 to determine the percent of data specified. 37. Less than = z 0.25 59.87% 38. Less than z 0.18 = − 42.86% 39. Greater than = − z 1.90 97.13% 40. Greater than = z 2.66 0.39% 41. Between = − z 1.84 and = z 1.84 93.42% 42. Between = − z 2.29 and = − z 1.33 8.08% 43. Between = z 1.96 and = z 2.14 0.88% 44. Between = − z 1.53 and = − z 1.82 2.86% 45. Between = z 0.72 and = z 2.14 21.96% 46. Between = − z 2.71 and = z 3.21 99.59% Problem Solving Heights of Girls In Exercises 47 and 48, assume that the heights of 7-year-old girls are normally distributed. The heights of 8 randomly selected 7-year-old girls are given in z-scores in the following table. Luisa0.9Jenny 0.0Heather–1.3Shenice 0.0 Sarah 1.7 Sadaf – 0.2 Eleanor 0.8 Kim-Liu –1.2 47. a) Which of these girls are taller than the mean? Luisa, Sarah, Eleanor b) Which of these girls are at the mean? Jenny, Shenice c) Which of these girls are shorter than the mean? Sadaf, Heather, Kim-Liu 48. a) Which girl is the tallest? Sarah b) Which girl is the shortest? Heather In Exercises 49–56, assume the average amount of caffeine consumed daily by adults is normally distributed with a mean of 250 mg and a standard deviation of 48 mg. 49. Determine the percent of adults who consume more than 250 mg of caffeine daily. 50% 50. Determine the percent of adults who consume more than 310 mg of caffeine daily. 10.56% 51. Determine the percent of adults who consume less than 250 mg of caffeine daily. 50% 52. Determine the percent of adults who consume less than 190 mg of caffeine daily. 10.56% 53. Determine the percent of adults who consume between 202 mg of caffeine and 346 mg of caffeine daily. 81.85% 54. Determine the percent of adults who consume between 154 mg of caffeine and 298 mg of caffeine daily. 81.85% 55. In a random sample of 500 adults, how many consume at least 310 mg of caffeine daily? 53adults ≈ 56. In a random sample of 500 adults, how many consume between 202 mg of caffeine and 346 mg of caffeine daily? 409 adults ≈ Hours Worked by College Students In Exercises 57– 62, assume the number of hours college students spend working per week is normally distributed with a mean of 20 hours and a standard deviation of 4 hours. 57. Determine the percent of college students who work less than 22 hours per week. 69.15% 58. Determine the percent of college students who work more than 27 hours per week. 4.01% 59. Determine the percent of college students who work between 14 and 26 hours per week. 86.64% 60. Determine the percent of college students who work between 18 and 30 hours per week. 68.53% 61. Determine the percent of college students who work more than 25 hours per week. 10.56% 62. Determine the percent of college students who work less than 10 hours per week. 0.62% Vending Machine In Exercises 63– 66, a vending machine is designed to dispense a mean of 7.6 oz of coffee into an 8-oz cup. If the standard deviation of the amount of coffee dispensed is 0.4 oz and the amount is normally distributed, determine the percent of times the machine will 63. dispense more than 7.0 oz. 93.32% 64. dispense less than 7.0 oz. 6.68% 65. dispense less than 7.7 oz. 59.87% 66. result in the cup overflowing (therefore dispense more than 8 oz). 15.87% Africa Studio/Shutterstock
RkJQdWJsaXNoZXIy NjM5ODQ=