Answer Questions 39-48

for all questions without a drawing, draw and shade the curve.

Using and Interpreting Concepts Using Normal Distributions In Exercises 39-44, answer the questions about the specified normal distribution. 39. Heights of Women In a survey of women in the United States (ages 20-29), the mean height was 64.1 inches with a standard deviation of 2.71 inches. (Adapted from National Center for Health Statistics) (a) What height represents the 95th percentile? (b) What height represents the first quartile? 40. Heights of Men In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. (Adapted from National Center for Health Statistics) (a) What height represents the 90th percentile? (b) What height represents the first quartile? 41. Apples The annual per capita utilization of apples (in pounds) in the United States can be approximated by a normal distribution, as shown in the graph. (Adapted from U.S. Department of Agriculture) (a) What annual per capita utilization of apples represents the 10th percentile? (b) What annual per capita utilization of apples represents the third quartile? Annual U.S. per Capita Annual U.S. per Capita Apple Utilization Orange Utilization M = 17.1 1b M = 11.4 1b 6 = 41b 0= 31b 5 9 13 17 21 25 29 8 11 14 17 20 Utilization (in pounds) Utilization (in pounds) FIGURE FOR EXERCISE 41 FIGURE FOR EXERCISE 42 42. Oranges The annual per capita utilization of oranges (in pounds) in the United States can be approximated by a normal distribution, as shown in the graph. (Adapted from U.S. Department of Agriculture) (a) What annual per capita utilization of oranges represents the 5th percentile? (b) What annual per capita utilization of oranges represents the third quartile?pent Waiting for 43. Heart Transplant Waiting Times The time spent (in days) waiting for a a Heart heart transplant in Ohio and Michigan for patients with type A blood can M = 127 days be approximated by a normal distribution, as shown in the graph. (Adapted "= 23.5 days from Organ Procurement and Transplant Network) (a) What is the shortest time spent waiting for a heart that would still place a patient in the top 30% of waiting times? (b) What is the longest time spent waiting for a heart that would still place 114 141 168 195 a patient in the bottom 10% of waiting times? Days R EXERCISE 43 44. Ice Cream The annual per capita consumption of ice cream (in pounds) in the United States can be approximated by a normal distribution, as shown in al U.S. per Capita the graph. (Adapted from U.S. Department of Agriculture) eam Consumption (a) What is the smallest annual per capita consumption of ice cream that can M = 15.4 1b be in the top 25% of consumptions? 6= 2.5 1b (b) What is the largest annual per capita consumption of ice cream that can be in the bottom 15% of consumptions? 45. Cereal Boxes The weights of the contents of a cereal box are normally distributed with a mean weight of 20 ounces and a standard deviation of 2 14 16 18 20 22 0.07 ounce. Boxes in the lower 5% do not meet the minimum weight umption (in pounds) bisonste requirements and must be repackaged. What is the minimum weight R EXERCISE 44 requirement for a cereal box? 46. Bags of Baby Carrots The weights of bags of baby carrots are normally distributed with a mean of 32 ounces and a standard deviation of 0.36 ounce. Sslins Bags in the upper 4.5% are too heavy and must be repackaged. What is the uog at aslags to none most a bag of baby carrots can weigh and not need to be repackaged? Extending Concepts 47. Writing a Guarantee You sell a brand of automobile tire that has a life einseiger zolags lo no expectancy that is normally distributed, with a mean life of 30,000 miles and a standard deviation of 2500 miles. You want to give a guarantee for free replacement of tires that don't wear well. How should you word your guarantee if you are willing to replace approximately 10% of the tires you sell? Exam Grades 48. Statistics Grades In a large section of a statistics class, the points for the final 40% exam are normally distributed with a mean of 72 and a standard deviation of 9. Grades are to be assigned according to the following rule. 20% . The top 10% receive As The next 20% receive Bs 10% . The middle 40% receive Cs . The next 20% receive Ds C B The bottom 10% receive Fs ored on final exam Find the lowest score on the final exam that would qualify a student for an R EXERCISE 48 A, a B, a C, and a D. 49. Vending Machine A vending machine dispenses coffee into an eight-ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.03 ounce. You can allow the cup to overfill 1% of the time. What amount should you set as the mean amount of coffee to be dispensed