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Stats Modeling The World AP Edition Grades 9-12 3rd Edition David E. Bock, Paul F. Velleman, Richard D. De Veaux - Solutions
Matching. Here and on the next page are several scatterplots. The calculated correlations are 0.736, and 0.951. Which is which?
Matching. Here are several scatterplots. The calculated correlations are and 0.777. Which is which?
Coffee sales. Owners of a new coffee shop tracked sales for the first 20 days and displayed the data in a scatterplot (by day):a) Make a histogram of the daily sales since the shop has been in business.b) State one fact that is obvious from the scatterplot, but not from the histogram.c) State one
Firing pottery. A ceramics factory can fire eight large batches of pottery a day. Sometimes a few of the pieces break in the process. In order to understand the problem better, the factory records the number of broken pieces in each batch for 3 days and then creates the scatterplot shown.a) Make a
Kentucky Derby 2006. The fastest horse in Kentucky Derby history was Secretariat in 1973. The scatterplot shows speed (in miles per hour) of the winning horses each year.What do you see? In most sporting events, performances have improved and continue to improve, so surely we anticipate a positive
Performance IQ scores vs. brain size. A study examined brain size (measured as pixels counted in a digitized magnetic resonance image [MRI] of a cross section of the brain) and IQ (4 Performance scales of the Weschler IQ test) for college students. The scatterplot shows the Performance IQ scores
Scatterplots. Which of the scatterplots below showa) little or no association?b) a negative association?c) a linear association?d) a moderately strong association?e) a very strong association?
Scatterplots. Which of the scatterplots at the top of the next column showa) little or no association?b) a negative association?c) a linear association?d) a moderately strong association?e) a very strong association?
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Crime and punishment. Because of the development of statistics and the methods of analysis you are learning about in this book, the 20th century has been called The First Measured Century in a series of documentaries on PBS. On the following page are two of their graphs.a) Write a few sentences
Some assembly required. A company that markets build-it-yourself furniture sells a computer desk that is advertised with the claim less than an hour to assemble. However, through postpurchase surveys the company has learned that only 25% of its customers succeeded in building the desk in under an
Profits. Here is a stem-and-leaf display showing profits as a percent of sales for 29 of the Forbes 500 largest U.S.corporations. The stems are split; each stem represents a span of 5%, from a loss of 9% to a profit of 25%.
Bike safety 2003. The Bicycle Helmet Safety Institute website includes a report on the number of bicycle fatalities per year in the United States. The table below shows the counts for the years 1994 2003.a) What are the W s for these data?b) Display the data in a stem-and-leaf display.c) Display
Public opinion. For many years Martha Stewart was a popular expert in home decorating, an arbiter of good taste, and a very successful businesswoman. In June 2002 she first came under attack amidst rumors of insider stock trading. At that time, a series of Gallup polls each contacted over 1000
Age and party II. Consider again the Pew Research Center results on age and political party in Exercise 33.a) What is the marginal distribution of party affiliation?b) Create segmented bar graphs displaying the conditional distribution of party affiliation for each age group.c) Summarize these poll
Engines, again. Horsepower is another measure commonly used to describe auto engines. Here are the summary statistics and histogram displaying horsepowers of the same group of 38 cars.
Age and party 2007. The Pew Research Center conducts surveys regularly asking respondents which political party they identify with. Among their results is the following table relating preferred political party and age.(http://people-press.org/reports/)a) What percent of people surveyed were
Pay. According to the 2006 National Occupational Employment and Wage Estimates for Management Occupations, the mean hourly wage for Chief Executives was $69.52 and the median hourly wage was over$70.00. By contrast, for General and Operations Managers, the mean hourly wage was $47.73 and the median
Herbal medicine. Researchers for the Herbal Medicine Council collected information on people s experiences with a new herbal remedy for colds. They went to a store that sold natural health products. There they asked 100 customers whether they had taken the cold remedy and, if so, to rate its
Birth order revisited. Consider again the data on birth order and college majors in Exercise 28.a) What is the marginal distribution of majors?b) What is the conditional distribution of majors for the oldest children?
Engines. One measure of the size of an automobile engine is its displacement, the total volume (in liters or cubic inches) of its cylinders. Summary statistics for several models of new cars are shown. These displacements were measured in cubic inches.
Birth order. Is your birth order related to your choice of major? A Statistics professor at a large university polled his students to find out what their majors were and what position they held in the family birth order. The results are summarized in the table.
Mail. Here are the number of pieces of mail received at a school office for 36 days.a) Plot these data.b) Find appropriate summary statistics.c) Write a brief description of the school s mail deliveries.d) What percent of the days actually lie within one standard deviation of the mean? Comment.
Music and memory. Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, Mozart, or no music while attempting to memorize objects pictured on a page. They were then asked to list
Sluggers. Roger Maris s 1961 home run record stood until Mark McGwire hit 70 in 1998. Listed below are the home run totals for each season McGwire played. Also listed are Babe Ruth s home run totals.
Sample. A study in South Africa focusing on the impact of health insurance identified 1590 children at birth and then sought to conduct follow-up health studies 5 years later. Only 416 of the original group participated in the 5-year follow-up study. This made researchers concerned that the
Winter Olympics 2006 speed skating. The top 25 women s 500-m speed skating times are listed in the table below:a) The mean finishing time was 78.21 seconds, with a standard deviation of 1.03 second. If the Normal model is appropriate, what percent of the times should be within 0.5 second of
Liberty s nose. Is the Statue of Liberty s nose too long?Her nose measures , but she is a large statue, after all. Her arm is 42 feet long. That means her arm is times as long as her nose. Is that a reasonable ratio? Shown in the table are arm and nose lengths of 18 girls in a Statistics class, and
Teen drivers. In its Traffic Safety Facts 2005, the National Highway Traffic Safety Administration reported that 6.3% of licensed drivers were between the ages of 15 and 20, yet this age group was behind the wheel in 15.9% of all fatal crashes. Use these statistics to explain the concept of
Old Faithful? Does the duration of an eruption have an effect on the length of time that elapses before the next eruption?a) The histogram below shows the duration (in minutes)of those 222 eruptions. Describe this distribution.
Old Faithful. It is a common belief that Yellowstone s most famous geyser erupts once an hour at very predictable intervals. The histogram below shows the time gaps (in minutes) between 222 successive eruptions.Describe this distribution.
Seasons. Average daily temperatures in January and July for 60 large U.S. cities are graphed in the histograms below.a) What aspect of these histograms makes it difficult to compare the distributions?b) What differences do you see between the distributions of January and July average
Hard water II. The data set from England and Wales also notes for each town whether it was south or north of Derby. Here are some summary statistics and a comparative boxplot for the two regions.a) What is the overall mean mortality rate for the two regions?b) Do you see evidence of a difference in
Hard water. In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in the
Accidents. In 2001, Progressive Insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. The data are summarized in the table.a) Create an appropriate graph of these data.b) Do these data indicate that driving near home is
Let s play cards. You pick a card from a deck (see description in Chapter 11) and record its denomination(7, say) and its suit (maybe spades).a) Is the variable suit categorical or quantitative?b) Name a game you might be playing for which you would consider the variable denomination to be
Computers and Internet. A U.S. Census Bureau report(August 2000, Current Population Survey) found that 51.0%of homes had a personal computer and 41.5% had access to the Internet. A newspaper concluded that 92.5% of homes had either a computer or access to the Internet. Do you agree? Explain.
Cramming. One Thursday, researchers gave students enrolled in a section of basic Spanish a set of 50 new vocabulary words to memorize. On Friday the students took a vocabulary test. When they returned to class the following Monday, they were retested without advance warning. Both sets of test
Streams. As part of the course work, a class at an upstate NY college collects data on streams each year. Students record a number of biological, chemical, and physical variables, including the stream name, the substrate of the stream (limestone, shale, or mixed), the pH, the temperature( ), and
Fraud detection. A credit card bank is investigating the incidence of fraudulent card use. The bank suspects that the type of product bought may provide clues to the fraud. To examine this situation, the bank looks at the Standard Industrial Code (SIC) of the business related to the transaction.
Acid rain. Based on long-term investigation, researchers have suggested that the acidity (pH) of rainfall in the Shenandoah Mountains can be described by the Normal model N(4.9, 0.6).a) Draw and carefully label the model.b) What percent of storms produce rainfall with pH over 6?c) What percent of
State University. Public relations staff at State U. collected data on people s opinions of various colleges and universities in their state. They phoned 850 local residents.After identifying themselves, the callers asked the survey participants their ages, whether they had attended college, and
Bread. Clarksburg Bakery is trying to predict how many loaves to bake. In the last 100 days, they have sold between 95 and 140 loaves per day. Here is a histogram of the number of loaves they sold for the last 100 days.a) Describe the distribution.b) Which should be larger, the mean number of sales
Beanstalks. Beanstalk Clubs are social clubs for very tall people. To join, a man must be over tall, and a woman over The National Health Survey suggests that heights of adults may be Normally distributed, with mean heights of for men and for women. The respective standard deviations are anda) You
Dialysis. In a study of dialysis, researchers found that of the three patients who were currently on dialysis, 67%had developed blindness and 33% had their toes amputated. What kind of display might be appropriate for these data? Explain.
Singers. The boxplots shown display the heights(in inches) of 130 members of a choir.
Prenatal care. Results of a 1996 American Medical Association report about the infant mortality rate for twins carried for the full term of a normal pregnancy are shown below, broken down by the level of prenatal care the mother had received.a) Is the overall rate the average of the other three
Bananas. Here are the prices (in cents per pound) of bananas reported from 15 markets surveyed by the U.S.Department of Agriculture.51 52 45 48 53 52 50 49 52 48 43 46 45 42 50a) Display these data with an appropriate graph.b) Report appropriate summary statistics.c) Write a few sentences about
Tomatoes. Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of Roma plants produces fruit that averages 74 grams, but 11% of the tomatoes
Eggs. Hens usually begin laying eggs when they are about 6 months old. Young hens tend to lay smaller eggs, often weighing less than the desired minimum weight of 54 grams.a) The average weight of the eggs produced by the young hens is 50.9 grams, and only 28% of their eggs exceed the desired
Trout. Wildlife biologists believe that the weights of adult trout can be described by a Normal model. They collected data from fishermen, finding that 22% of the trout caught were thrown back because they were below the 2-pound minimum, and only 6% weighed over 5 pounds. What mean and standard
First steps. While only 5% of babies have learned to walk by the age of 10 months, 75% are walking by 13 months of age. If the age at which babies develop the ability to walk can be described by a Normal model, find the parameters (mean and standard deviation).
Big mouth! A Cornell University researcher measured the mouth volumes of 31 men and 30 women. She found a mean of 66 cc for men (SD = 17 cc) and a mean of 54 cc for women (SD = 14.5 cc). The man with the largest mouth had a mouth volume of 111.2 cc. The woman with the largest mouth had a mouth
Undercover? We learned in the chapter that the average Dutch man is 184 cm tall. The standard deviation of Caucasian adult male heights is about 7 cm. The average Greek 18-year-old in Athens is 167.8 cm tall. How easily could the average Dutch man hide in Athens? (Let s assume he dyes his hair, if
Body temperatures. Most people think that the normal adult body temperature is That figure, based on a 19th-century study, has recently been challenged. In a 1992 article in the Journal of the American Medical Association, researchers reported that a more accurate figure may be Furthermore, the
Kindergarten. Companies that design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 38.2 inches and standard deviation of 1.8 inches.a) What fraction of
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 a set of these tires, would it be reasonable for you to hope they ll last 40,000 miles? Explain.b) Approximately
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
Parameters II. Every Normal model is defined by its parameters: the mean and the standard deviation. For each model described below, find the missing parameter.Don t forget to draw a picture.a)b)c)d)
Parameters. Every Normal model is defined by its parameters: the mean and the standard deviation. For each model described below, find the missing parameter. As always, start by drawing a picture.a)b)c)d)
IQ, finis. Consider the IQ model N(100, 16) 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?
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?
More IQs. In the Normal model N(100, 16), what cutoff value boundsa) the highest 5% of all IQs?b) the lowest 30% of the IQs?c) the middle 80% of the IQs?
More cattle. Based on the model N(1152, 84) describing Angus steer weights, what are the cutoff values fora) the highest 10% of the weights?b) the lowest 20% of the weights?c) the middle 40% of the weights?
IQs revisited. Based on the Normal model N(100, 16)describing IQ scores, what percent of people s IQs would you expect to bea) over 80?b) under 90?c) between 112 and 132?
Normal cattle. Using N(1152, 84), the Normal model for weights of Angus steers in Exercise 19, what percent of steers weigha) over 1250 pounds?b) under 1200 pounds?c) between 1000 and 1100 pounds?
Yet another Normal model. In a standard Normal model, what value(s) of z cut(s) off the region described?Remember to draw a picture first.a) the lowest 12%b) the highest 30%c) the highest 7%d) the middle 50%
More Normal models. In a standard Normal model, what value(s) of z cut(s) off the region described? Don t forget to draw a picture.a) the highest 20%b) the highest 75%c) the lowest 3%d) the middle 90%
Normal models, again. What percent of a standard Normal model is found in each region? Draw a picture first.a)b)c)d)
Normal models. What percent of a standard Normal model is found in each region? Be sure to draw a picture first.a)b)c)d)
Customer database. A large philanthropic organization keeps records on the people who have contributed to their cause. In addition to keeping records of past giving, the organization buys demographic data on neighborhoods from the U.S. Census Bureau. Eighteen of these variables concern the
Receivers. NFL data from the 2006 football season reported the number of yards gained by each of the league s 167 wide receivers:The mean is 435 yards, with a standard deviation of 384 yards.a) According to the Normal model, what percent of receivers would you expect to gain fewer yards than 2
Check the model. Recall from Exercise 20 that the mean of the 100 car speeds in Exercise 34 was 23.84 mph, with a standard deviation of 3.56 mph.a) Using a Normal model, what values should border the middle 95% of all car speeds?b) Here are some summary statistics.From your answer in parta, how
Trees, part II. Later on, the forester in Exercise 33 shows you a histogram of the tree diameters he used in analyzing the woods that was for sale. Do you think he was justified in using a Normal model? Explain, citing some specific concerns.
Car speeds, the picture. For the car speed data of Exercise 20, here is the histogram, boxplot, and Normal probability plot of the 100 readings. Do you think it is appropriate to apply a Normal model here? Explain.
Trees. A forester measured 27 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal model applies.a) Draw the Normal model for
Rivets. A company that manufactures rivets believes the shear strength (in pounds) is modeled by N(800, 50).a) Draw and label the Normal model.b) Would it be safe to use these rivets in a situation requiring a shear strength of 750 pounds? Explain.c) About what percent of these rivets would you
Winter Olympics 2006 downhill. Fifty-three men qualified for the men s alpine downhill race in Torino.The gold medal winner finished in 1 minute, 48.8 seconds. All competitors times (in seconds) are found in the following list:
High IQ. Exercise 28 proposes modeling IQ scores with N(100, 16). What IQ would you consider to be unusually high? Explain.
Small steer. In Exercise 19 we suggested the model N(1152, 84) for weights in pounds of yearling Angus steers. What weight would you consider to be unusually low for such an animal? Explain.
IQ. Some IQ tests are standardized to a Normal model, with a mean of 100 and a standard deviation of 16.a) Draw the model for these IQ scores. Clearly label it, showing what the 68 95 99.7 Rule predicts about the scores.b) In what interval would you expect the central 95%of IQ scores to be found?c)
Guzzlers? Environmental Protection Agency (EPA)fuel economy estimates for automobile models tested recently predicted a mean of 24.8 mpg and a standard deviation of 6.2 mpg for highway driving. Assume that a Normal model can be applied.a) Draw the model for auto fuel economy. Clearly label it,
Rock concerts. A popular band on tour played a series of concerts in large venues. They always drew a large crowd, averaging 21,359 fans. While the band did not announce (and probably never calculated) the standard deviation, which of these values do you think is most likely to be correct: 20, 200,
Professors. A friend tells you about a recent study dealing with the number of years of teaching experience among current college professors. He remembers the mean but can t recall whether the standard deviation was 6 months, 6 years, or 16 years. Tell him which one it must have been, and why.
Caught speeding. Suppose police set up radar surveillance on the Stanford street described in Exercise 20.They handed out a large number of tickets to speeders going a mean of 28 mph, with a standard deviation of 2.4 mph, a maximum of 33 mph, and an IQR of 3.2 mph. Local law prescribes fines of
Cattle, part III. Suppose the auctioneer in Exercise 21 sold a herd of cattle whose minimum weight was 980 pounds, median was 1140 pounds, standard deviation 84 pounds, and IQR 102 pounds. They sold for 40 cents a pound, and the auctioneer took a $20 commission on each animal. Then, for example, a
Car speeds again. For the car speed data of Exercise 20, recall that the mean speed recorded was 23.84 mph, with a standard deviation of 3.56 mph. To see how many cars are speeding, John subtracts 20 mph from all speeds.a) What is the mean speed now? What is the new standard deviation?b) His friend
More cattle. Recall that the beef cattle described in Exercise 19 had a mean weight of 1152 pounds, with a standard deviation of 84 pounds.a) Cattle buyers hope that yearling Angus steers will weigh at least 1000 pounds. To see how much over(or under) that goal the cattle are, we could subtract
Car speeds. John Beale of Stanford, CA, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. The mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (He actually recorded every car for a two-month period. These are 100 representative
Cattle. The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds.Suppose that weights of all such animals can be described by a Normal model with a standard deviation of 84 pounds.a) How many standard deviations from the mean would a steer weighing
MP3s. Two companies market new batteries targeted at owners of personal music players. DuraTunes claims a mean battery life of 11 hours, while RockReady advertises 12 hours.a) Explain why you would also like to know the standard deviations of the battery lifespans before deciding which brand to
Final exams. Anna, a language major, took final exams in both French and Spanish and scored 83 on each. Her roommate Megan, also taking both courses, scored 77 on the French exam and 95 on the Spanish exam. Overall, student scores on the French exam had a mean of 81 and a standard deviation of 5,
Combining scores again. The first Stat exam had a mean of 80 and a standard deviation of 4 points; the second had a mean of 70 and a standard deviation of 15 points. Reginald scored an 80 on the first test and an 85 on the second. Sara scored an 88 on the first but only a 65 on the second. Although
Combining test scores. The first Stats exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Julie scored a 70 on the first test and a 90 on the second. They both totaled 160 points on the
Placement exams. An incoming freshman took her college s placement exams in French and mathematics. In French, she scored 82 and in math 86. The overall results on the French exam had a mean of 72 and a standard deviation of 8, while the mean math score was 68, with a standard deviation of 12. On
Temperatures. A town s January high temperatures average with a standard deviation of , while in July the mean high temperature is and the standard deviation is . In which month is it more unusual to have a day with a high temperature of ? Explain.
Mensa. People with z-scores greater than 2.5 on an IQ test are sometimes classified as geniuses. If IQ test scores have a mean of 100 and a standard deviation of 16 points, what IQ score do you need to be considered a genius?
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