258 CHAPTER 5 Normal Probability Distributions Using and Interpreting Concepts Finding Specified Data Values In Exercises 31–38, answer the questions about the specified normal distribution. 31. Weights of Teenagers In a survey of 18-year old males, the mean weight was 166.7 pounds with a standard deviation of 49.3 pounds. (Adapted from National Center for Health Statistics) (a) What weight represents the 95th percentile? (b) What weight represents the 43rd percentile? (c) What weight represents the first quartile? 32. COVID-19 Response Surveyors asked respondents to rate ten key aspects of their government’s response to the COVID-19 pandemic, including preparedness, communication, and material aid. A pandemic response score that ranged from 0 to 100 was calculated. The mean score for U.S. respondents was 50.6 with a standard deviation of 29.0. (Source: PLOS One) (a) What score represents the 88th percentile? (b) What score represents the 61st percentile? (c) What score represents the first quartile? 33. Billboard Hot 100 The length (in seconds) of the 100 most popular songs during the week of May 5, 2021, can be approximated by a normal distribution, as shown in the figure. (Source: Spotify) (a) What song length represents the 5th percentile? (b) What song length represents the 17th percentile? (c) What song length represents the third quartile? x = 187.9 s μ = 32.8 s σ Seconds Billboard Hot 100 Song Lengths 100 150 200 250 x = 1.34 m3/kg μ = 0.80 m3/kg σ Cubic meters Water Footprint of Wheat in the U.S. 0 1 2 3 FIGURE FOR EXERCISE 33 FIGURE FOR EXERCISE 34 34. Water Footprint A water footprint is a measure of the appropriation of fresh water. The water footprint (in cubic meters) for a kilogram of wheat can be approximated by a normal distribution, as shown in the figure. (Source: Ecological Indicators) (a) What water footprint represents the 80th percentile? (b) What water footprint represents the 29th percentile? (c) What water footprint represents the third quartile? 35. Advanced Dental Admission Test The Advanced Dental Admission Test (ADAT) is designed so that the scores fit a normal distribution, as shown in the figure. (Source: American Dental Association) (a) What is the minimum ADAT score that is in the top 5% of scores? (b) Between what two values does the middle 50% of the ADAT scores lie? x = 500 μ = 100 σ Advanced Dental Admission Test Score 200 400 600 800 FIGURE FOR EXERCISE 35
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