Section 3.3 Measures of Position 137 a. Find the z-score for an ACT score of 25. b. Find the z-score for an SAT math score of 650. c. Which score is higher, relative to its population of scores? d. Jose’s ACT score had a z-score of 1.98. What was his ACT score? e. Emma’s SAT score had a z-score of −1.5. What was her SAT score? 22. A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 126 with standard deviation of 18, and the mean length of two-year-old spotted flounder is 162 with a standard deviation of 28. The distribution of flounder lengths is approximately bell-shaped. a. Anna caught a one-year-old flounder that was 150 millimeters in length. What is the z-score for this length? b. Luis caught a two-year-old flounder that was 190 millimeters in length. What is the z-score for this length? c. Whose fish is longer, relative to fish the same age? d. Joe caught a one-year-old flounder whose length had a z-score of 1.2. How long was this fish? e. Terry caught a two-year-old flounder whose length had a z-score of −0.5. How long was this fish? Source: Turkish Journal of Veterinary and Animal Science, 29:1013–1018 23. Blood pressure in men: The three quartiles for systolic blood pressure in a sample of 3179 men were Q1 = 108, Q2 = 116, and Q3 = 127. a. Find the IQR. b. Find the upper and lower outlier boundaries. c. A systolic blood pressure greater than 140 is considered high. Would a blood pressure of 140 be an outlier? Source: Journal of Human Hypertension, 16:305–312 24. Blood pressure in women: The article referred to in Exercise 23 reported that the three quartiles for systolic blood pressure in a sample of 1213 women between the ages of 20 and 29 were Q1 = 100, Q2 = 108, and Q3 = 115. a. Find the IQR. b. Find the upper and lower outlier boundaries. c. A systolic blood pressure greater than 140 is considered high. Would a blood pressure of 140 be an outlier? 25. Hazardous waste: Following is a list of the number of hazardous waste sites in each of the 50 states of the United States in a recent year. The list has been sorted into numerical order. 0 1 2 2 3 5 6 9 9 9 9 9 11 12 12 12 12 12 13 13 14 14 14 14 15 15 15 16 19 19 20 21 25 26 29 30 32 32 32 38 40 48 49 49 52 67 86 97 97 116 Source: U.S. Environmental Protection Agency a. Find the first and third quartiles of these data. b. Find the median of these data. c. Find the upper and lower outlier boundaries. d. Are there any outliers? If so, list them. e. Construct a boxplot for these data. f. Describe the shape of this distribution. g. What is the 30th percentile? h. What is the 85th percentile? i. The state of Georgia has 16 hazardous waste sites. What percentile is this? 26. Cholesterol levels: The National Health and Nutrition Examination Survey (NHANES) measured the serum HDL cholesterol levels in a large number of women. Following is a sample of 40 HDL levels (in milligrams per deciliter) that are based on the results of that survey. They have been sorted into numerical order. 27 28 30 32 34 36 37 37 37 37 37 40 45 47 48 49 53 53 54 56 57 58 61 62 63 63 64 64 64 65 66 70 72 73 73 74 80 80 81 84 Source: NHANES a. Find the first and third quartiles of these data. b. Find the median of these data. c. Find the upper and lower outlier boundaries. d. Are there any outliers? If so, list them. e. Construct a boxplot for these data. f. Describe the shape of this distribution. g. What is the 20th percentile? h. What is the 67th percentile? i. One woman had a cholesterol level of 58. What percentile is this? 27. Commuting to work: Jamie drives to work every weekday morning. She keeps track of the time it takes, in minutes, for 35 days. The results follow. 15 17 17 17 17 18 19 19 19 19 19 19 20 20 20 20 20 21 21 21 21 21 21 21 21 21 22 23 23 24 26 31 36 38 39 a. Find the first and third quartiles of these data. b. Find the median of these data. c. Find the upper and lower outlier boundaries. d. Are there any outliers? If so, list them. e. Construct a boxplot for these data. f. Describe the shape of this distribution. g. What is the 14th percentile? h. What is the 87th percentile? i. One day, the commute time was 31 minutes. What percentile is this? 28. Windy city by the bay: Following are wind speeds (in mph) for 29 randomly selected days in San Francisco. 13.4 23.1 27.2 31.8 36.3 40.3 14.1 24.6 27.7 32.6 38.1 40.9 18.3 25.2 29.7 33.6 38.7 44.2 20.8 26.8 30.1 34.5 40.2 46.8 22.9 26.9 30.8 35.8 40.3 a. Find the first and third quartiles of these data. b. Find the median of these data. c. Find the upper and lower outlier boundaries. d. Are there any outliers? If so, list them. e. Construct a boxplot for these data. f. Describe the shape of this distribution. g. What is the 40th percentile? h. What is the 10th percentile? i. One day, the wind speed was 30.1 mph. What percentile is this?
navidi_monk_essential_statistics_1e_ch1_3
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