49. Super Bowl points 2016 How many points do football teams score in the Super Bowl? Here are the total numbers of points scored by both teams in each of the first 50 Super Bowl games. (Data in Super Bowl 2016) 45, 47, 23, 30, 29, 27, 21, 31, 22, 38, 46, 37, 66, 50, 37, 47, 44, 47, 54, 56, 59, 52, 36, 65, 39, 61, 69, 43, 75, 44, 56, 55, 53, 39, 41, 37, 69, 61, 45, 31, 46, 31, 50, 48, 56, 38, 65, 51, 52, 34 a) Find the median. b) Find the quartiles. c) Make a histogram and write a brief description of the distri- bution. 50. Super Bowl edge 2016 In the Super Bowl, by how many points does the winning team outscore the losers? Here are the winning margins for the first 50 Super Bowl games. (Data in Super Bowl 2016) 25, 19, 9, 16, 3, 21, 7, 17, 10, 4, 18, 17, 4, 12, 17, 5, 10, 29, 22, 36, 19, 32, 4, 45, 1, 13, 35, 17, 23, 10, 14, 7, 15, 7, 27, 3, 27, 3, 3, 11, 12, 3, 4, 14, 6, 4, 3, 35, 4, 14 a) Find the median. b) Find the quartiles. c) Make a histogram and write a brief description of the distribution. 51. Test scores, large class Test scores from a large calculus class of 400 are shown in the histogram below. # of Students 100 80 40 error will affect these summary statistics for the company payroll: a) measures of center: median and mean b) measures of spread: range, IQR, and standard deviation 54. Sick days During contract negotiations, a company seeks to change the number of sick days employees may take, saying that the annual "average" is 7 days of absence per employee. The union negotiators counter that the "average" employee misses only 3 days of work each year. a) Explain how both sides might be correct, identifying the measure of center you think each side is using and why the difference might exist. b) Do their choices of summaries make sense? 55. Floods 2015 Here are the annual numbers of deaths from floods in the United States from 1995 through 2015: 80, 131, 118, 136, 68, 38, 48, 49, 86, 82, 43, 76, 87, 82, 56, 103, 113, 29, 82, 38, 176 Find these statistics: a) mean b) median and quartiles c) range and IQR 56. Tornadoes 2015 Here are the annual numbers of deaths from tornadoes in the United States from 1995 through 2015: 30, 25, 67, 130, 94, 41, 40, 55, 54, 35, 38, 67, 81, 126, 21, 45, 553, 70, 55, 47, 36 Find these statistics: a) mean b) median and quartiles c) range and IOR at a laige university Classifitu uit vialus by commuy of ongi, as seen in the table. Origin Driver Student Staff American 107 105 European 33 12 Asian 55 47 a) What percent of all the cars surveyed were foreign? b) What percent of the American cars were owned by students? c) What percent of the students owned American cars? d) What is the marginal distribution of origin? e) What are the conditional distributions of origin by driver classification? f) Do you think that the origin of the car is independent of the type of driver? Explain. 39. Weather forecasts Just how accurate are the weather forecasts we hear every day? The following table compares the daily forecast with a city's actual weather for a year: Forecast Actual Weather Rain No Rain Rain 27 63 No Rain 7 268 a) On what percent of days did it actually rain? b) On what percent of days was rain predicted? c) What percent of the time was the forecast correct? d) Do you see evidence of an association between the type of T T Cafe Quing with pregnancies: b) What percent of all twin births were preterm? c) Among the mothers who received inadequate medical care, what percent of the twin births were preterm? d) Create an appropriate graph comparing the outcomes of these pregnancies by the level of medical care the mother received. e) Write a few sentences describing the association between these two variables. 41. Blood pressure A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by Age and Blood pressure: Blood Pressure Age Under 30 30-49 Over 50 Low 27 37 31 Normal 48 91 93 High 23 51 73 a) Find the marginal distribution of blood pressure level. b) Find the conditional distribution of blood pressure level within each age group. c) Compare these distributions with a segmented bar graph. d) Write a brief description of the association between age and blood pressure among these employees. e) Does this prove that people's blood pressure increases as they age? Explain. 42. Obesity and exercise The Centers for Disease Control and Prevention (CDC) has estimated that 19.8% of Americans over 15 years old are obese. The CDC conducts a survey on obesity and various behaviors. Here is a table on self-reported exercise classified by body mass index (BMI): at a laige university Classifitu uit vialus by commuy of ongi, as seen in the table. Origin Driver Student Staff American 107 105 European 33 12 Asian 55 47 a) What percent of all the cars surveyed were foreign? b) What percent of the American cars were owned by students? c) What percent of the students owned American cars? d) What is the marginal distribution of origin? e) What are the conditional distributions of origin by driver classification? f) Do you think that the origin of the car is independent of the type of driver? Explain. 39. Weather forecasts Just how accurate are the weather forecasts we hear every day? The following table compares the daily forecast with a city's actual weather for a year: Forecast Actual Weather Rain No Rain Rain 27 63 No Rain 7 268 a) On what percent of days did it actually rain? b) On what percent of days was rain predicted? c) What percent of the time was the forecast correct? d) Do you see evidence of an association between the type of T T Cafe Quing with pregnancies: b) What percent of all twin births were preterm? c) Among the mothers who received inadequate medical care, what percent of the twin births were preterm? d) Create an appropriate graph comparing the outcomes of these pregnancies by the level of medical care the mother received. e) Write a few sentences describing the association between these two variables. 41. Blood pressure A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by Age and Blood pressure: Blood Pressure Age Under 30 30-49 Over 50 Low 27 37 31 Normal 48 91 93 High 23 51 73 a) Find the marginal distribution of blood pressure level. b) Find the conditional distribution of blood pressure level within each age group. c) Compare these distributions with a segmented bar graph. d) Write a brief description of the association between age and blood pressure among these employees. e) Does this prove that people's blood pressure increases as they age? Explain. 42. Obesity and exercise The Centers for Disease Control and Prevention (CDC) has estimated that 19.8% of Americans over 15 years old are obese. The CDC conducts a survey on obesity and various behaviors. Here is a table on self-reported exercise classified by body mass index (BMI): 30 50 12.372 13.243 14.115 14.986 15.858 e) The standard deviation of these means is 0.60. Does the 68-95-99.7 Rule give a good idea of the middle 95% of the distribution? 48. CEO compensation logged and sampled Suppose we take logarithms of the CEO compensations in Exercise 47. The his- togram of log Compensation looks like this: # of CEOs 80 60 60 10 20 20 0.1 0.6 1.1 1.6 2.1 Log CEO Compensation with a mean of 1.07 and a standard deviation of 0.26. a) According to the Normal model, what percent of CEOs would you expect to earn more than 2 standard deviations above the mean compensation? what cutoff value bounds a) the highest 5% of all IQs? b) the lowest 30% of the IQs? c) the middle 80% of the IQs? 51. Cattle, finis Consider the Angus weights model N(1152, 84) one last time. a) What weight represents the 40th percentile? b) What weight represents the 99th percentile? c) What's the IQR of the weights of these Angus steers? 52. IQ, finis Consider the IQ model N(100, 15) one last time. a) What IQ represents the 15th percentile? b) What IQ represents the 98th percentile? c) What's the IQR of the IQs? 53. Cholesterol Assume the cholesterol levels of adult American women can be described by a Normal model with a mean of 188 mg/dL and a standard deviation of 24. a) Draw and label the Normal model. b) What percent of adult women do you expect to have cholesterol levels over 200 mg/dL? c) What percent of adult women do you expect to have cholesterol levels between 150 and 170 mg/dL? d) Estimate the IQR of the cholesterol levels. e) Above what value are the highest 15% of women's cholesterol levels? 54. Tires A tire manufacturer believes that the treadlife of its snow tires can be described by a Normal model with a mean of 32,000 miles and standard deviation of 2500 miles. a) If you buy one of these tires, would it be reasonable for you to hope it will last 40,000 miles? Explain.