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intro stats

Questions and Answers of Intro Stats

Bread Clarksburg Bakery is trying to predict how many loaves to bake. In the past 100 days, they have sold between 95 and 140 loaves per day. Here is a histogram of the number of loaves they sold for
Beanstalks Beanstalk Clubs are social clubs for very tall people. To join, a man must be over 62 tall, and a woman over 510. The National Health Survey suggests that heights of adults may be
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
Singers by parts The boxplots shown display the heights(in inches) of 130 members of the choir we saw in Exercise 3.40. Now we have information about what part they sing.a) It appears that the median
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 on the next page, broken down
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
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.
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 43 grams.a) The average weight of the
Body temperatures Most people think that the“normal” adult body temperature is 98.6°F. That figure, based on a 19th-century study, has recently been challenged.In a 1992 article in the Journal
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
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
Cholesterol Assume the cholesterol levels of adult American women can be described by a Normal model with a mean of 196 mg/dL and a standard deviation of 27.a) Draw and label the Normal model.b) What
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
More IQs In the Normal model N(100, 16) from Exercise 2, 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 from Exercise 25, what are the cutoff values fora) the highest 10% of the weights?b) the lowest 20% of the weights?c) the
Customer database A large philanthropic organization keeps records on the people who have contributed. In addition to keeping records of past giving, the organization buys demographic data on
Receivers 2013 NFL data from the 2013 football season reported the number of yards gained by each of the league’s 181 wide receivers:The mean is 426.98 yards, with a standard deviation of 408.34
Check the model The mean of the 100 car speeds in Exercise 26 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
Winter Olympics 2010 downhill Fifty-nine men completed the men’s alpine downhill race in Vancouver.The gold medal winner finished in 114.3 seconds.Here are the times (in seconds) for all
Car speeds, the picture For the car speed data in Exercise 26, here is the histogram, boxplot, and Normal probability plot of the 100 readings. Do you think it is appropriate to apply a Normal model
Trees, part II Later on, the forester in Exercise 35 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
Rivets A company that manufactures rivets believes the shear strength (in pounds) is modeled by N(700, 40).a) Draw and label the Normal model.b) Would it be safe to use these rivets in a situation
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
High IQ Exercise 8, proposes modeling IQ scores with N(100, 16). What IQ would you consider to be unusually high? Explain.
Small steer In Exercise 25, 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.
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)
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
Caught speeding Suppose police set up radar surveillance on the Stanford street described in Exercise 26.They handed out a large number of tickets to speeders going a mean of 28 mph, with a standard
Cattle, part III Suppose the auctioneer in Exercise 27 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
Car speeds again For the car speed data in Exercise 26, 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
More cattle Recall that the beef cattle described in Exercise 25 had a mean weight of 1152 pounds, with a standard deviation of 84 pounds.a) Cattle buyers hope that yearling Angus steers will weigh
Car speeds John Beale of Stanford, California, 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
Cattle Using N(1152, 84), the Normal model for weights of Angus steers in Exercise 9,a) How many standard deviations from the mean would a steer weighing 1000 pounds be?b) Which would be more
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
Final exams Anna, a language major, took final exams in both French and Spanish and scored 87 on each. Her roommate Megan, also taking both courses, scored 79 on the French exam and 94 on the Spanish
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
Combining test scores The first Stats exam had a mean of 65 and a standard deviation of 15 points; the second had a mean of 85 and a standard deviation of 10 points.Derrick scored an 85 on both
Windy In the last chapter, we looked at three outliers arising from a plot of Average Wind Speed by Month in the Hopkins Forest. Each was associated with an unusually strong storm, but which was the
Music library again Corey has 4929 songs in his computer’s music library. The songs have a mean duration of 242.4 seconds with a standard deviation of 114.51 seconds. On the Nickel, by Tom Waits,
Checkup One of the authors has an adopted grandson whose birth family members are very short. After examining him at his 2-year checkup, the boy’s pediatrician said that the z-score for his height
Stats test, part II Suppose your Statistics professor reports test grades as z-scores, and you got a score of 2.20 on an exam. Write a sentence explaining what that means.
Cold U? A high school senior uses the Internet to get information on February temperatures in the town where he’ll be going to college. He finds a website with some statistics, but they are given
SAT or ACT? Each year thousands of high school students take either the SAT or the ACT, standardized tests used in the college admissions process. Combined SAT Math and Verbal scores go as high as
Hams A specialty foods company sells “gourmet hams” by mail order. The hams vary in size from 4.15 to 7.45 pounds, with a mean weight of 6 pounds and standard deviation of 0.65 pounds. The
Payroll Here are the summary statistics for the weekly payroll of a small company: lowest salary = +350, mean salary = +700, median = +700, range = +1200, IQR = +700, first quartile = +450, standard
Wisconsin ACT math The histogram shows the distribution of mean ACT mathematics scores for all Wisconsin public schools in 2011. The vertical lines show the mean and one standard deviation above and
Music library Corey has 4929 songs in his computer’s music library. The lengths of the songs have a mean of 242.4 seconds and standard deviation of 114.51 seconds.A Normal probability plot of the
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 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
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
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.
Hotline A company’s customer service hotline handles many calls relating to orders, refunds, and other issues.The company’s records indicate that the median length of calls to the hotline is 4.4
Shipments A company selling clothing on the Internet reports that the packages it ships have a median weight of 68 ounces and an IQR of 40 ounces.a) The company plans to include a sales flyer
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
Temperatures A town’s January high temperatures average 36°F with a standard deviation of 10°, while in July the mean high temperature is 74° and the standard deviation is 8°. In which month is
Mensa People with z-scores above 2.5 on an IQ test are sometimes classified as geniuses. If IQ scores have a mean of 100 and a standard deviation of 16 points, what IQ score do you need to be
Stats test The mean score on the Stats exam was 75 points with a standard deviation of 5 points, and Gregor’s z-score was -2. How many points did he score?
In the 2010 Winter Olympics men’s slalom, Li Lei of China skied in a total time of 120.86 sec for two runs—about 1 standard deviation slower than the mean.If a Normal model is useful in
Many colleges and universities require applicants to submit scores on standardized tests such as the SAT Writing, Math, and Critical Reading (Verbal)tests. The college your little sister wants to
The times in the men’s combined event at the winter Olympics are reported in minutes and seconds. The mean and standard deviation of the 34 final super combined times at the 2010 Olympics were
At the 2010 Vancouver Winter Olympics, Bode Miller had earlier earned a bronze medal in the downhill and a silver medal in the super-G slalom before winning the gold in the men’s super combined.
The men’s super combined skiing event debuted in the 2010 Winter Olympics in Vancouver. It consists of two races: a downhill and a slalom. Times for the two events are added together, and the skier
Stereograms, revisited Because of the skewness of the distributions of fusion times described in Exercise 51, we might consider a re-expression. Here are the boxplots of the log of fusion times. Is
Stereograms Stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional (3D) image by staring at the dots
Rainmakers The table lists the amount of rainfall (in acre-feet) from the 26 clouds seeded with silver iodide discussed in Exercise 40:a) Why is acre-feet a good way to measure the amount of
Assets again Here are the same data you saw in Exercise 47 after re-expressions as the square root of assets(in $M) and the logarithm of assets (in $M):a) Which re-expression do you prefer? Why?b) In
Music library Students were asked how many songs they had in their digital music libraries. Here’s a display of the responses:a) What aspect of this distribution makes it difficult to summarize, or
Assets Here is a histogram of the assets (in millions of dollars) of 79 companies chosen from the Forbes list of the nation’s top corporations:a) What aspect of this distribution makes it difficult
Drunk driving Accidents involving drunk drivers account for a large portion of all deaths on the nation’s highways.The table in the next column tracks the number of alcohol-related fatalities for
Fruit flies Researchers tracked a population of 1,203,646 fruit flies, counting how many died each day for 171 days.Here are three timeplots offering different views of these data. One shows the
Baseball 2013 American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The League believes that replacing the pitcher, typically a weak
MPG A consumer organization wants to compare gas mileage figures for several models of cars made in the United States with autos manufactured in other countries.The data for a random sample of cars
Cholesterol and Smoking A study examining the health risks of smoking measured the cholesterol levels of people who had smoked for at least 25 years and people of similar ages who had smoked for no
Industrial experiment Engineers at a computer production plant tested two methods for accuracy in drilling holes into a PC board. They tested how fast they could set the drilling machine by running
Cloud seeding In an experiment to determine whether seeding clouds with silver iodide increases rainfall, 58 clouds were randomly assigned to be seeded or not.The amount of rain they generated was
Reading scores A class of fourth graders takes a diagnostic reading test, and the scores are reported by reading grade level. The 5-number summaries for the 14 boys and 11 girls are shown:a) Which
Cholesterol The Framingham Heart Study recorded the cholesterol levels of more than 1400 men. Here is an ogive of the distribution of these cholesterol measures.(An ogive shows the percentage of
Derby speeds 2014 (Data in Kentucky Derby 2014)How fast do horses run? Kentucky Derby winners top 30 miles per hour, as shown in this graph. The graph shows the percentage of Derby winners that have
SAT scores Here are the summary statistics for Verbal SAT scores for a high school graduating class:a) Create side-by-side boxplots comparing the scores of boys and girls as best you can from the
Caffeine A student study of the effects of caffeine asked volunteers to take a memory test 2 hours after drinking soda. Some drank caffeine-free cola, some drank regular cola (with caffeine), and
Vineyards revisted Here are summary statistics for the sizes (in acres) of the Finger Lakes vineyards (of Exercise 3.17):Suppose you didn’t have access to the data. answer the following questions
Graduation? A survey of major universities asked what percentage of incoming freshmen usually graduate “on time” in 4 years. Use the summary statistics given to answer the questions that
Eye and hair color A survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. Two of the questions concerned eye and hair color. In
Test scores Three Statistics classes all took the same test.Histograms and boxplots of the scores for each class are shown below. Match each class with the corresponding boxplot. # of Students 2 4 30
Ozone Ozone levels (in parts per billion, ppb) were recorded at sites in New Jersey monthly between 1926 and 1971. Here are boxplots of the data for each month (over the 46 years), lined up in
Fuel economy 2012 The Environmental Protection Agency provides fuel economy and pollution information on over 2000 car models. Here is a boxplot of Combined Fuel Economy (using an average of driving
Fuel economy by cylinders Describe what these boxplots tell you about the relationship between the number of cylinders a car’s engine has and the car’s fuel economy (mpg). 35 30 Fuel Efficiency
Marriage age In 1975, did men and women marry at the same age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show.
Gas prices 2013 Here are boxplots of weekly gas prices for regular gas in the United States as reported by the U.S. Energy Information Administration for 2009 through 2013.a) Compare the distribution
Women’s basketball Here are boxplots of the points scored during the first 10 games of the season for both Scyrine and Alexandra:a) Summarize the similarities and differences in their performance
Deaths 2011 A National Vital Statistics Report(www.cdc.govchs/) indicated that nearly 290,000 black Americans died in 2011, compared with just over 2 million white Americans. Below are histograms
Hospital stays The U.S. National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals and publishes its findings in Vital and Health Statistics. Data
Camp sites Shown below are the histogram and summary statistics for the number of camp sites at public parks in Vermont.a) Which statistics would you use to identify the center and spread of this
Population growth 2010 by region On the next page is a “back-to-back” stem-and-leaf display that shows two data sets at once—one going to the left, one to the right.The display compares the
Tendon transfers People with spinal cord injuries may lose function in some, but not all, of their muscles.The ability to push oneself up is particularly important for shifting position when seated
Cereals Sugar is a major ingredient in many breakfast cereals. The histogram displays the sugar content as a percentage of weight for 49 brands of cereal. The boxplots compare sugar content for adult
Slalom times 2010 The Men’s Giant Slalom skiing event consists of two runs whose times are added together for a final score. Two displays of the giant slalom times in the 2010 Winter Olympics are
Rock concert accidents Crowd Management Strategies(www.crowdsafe.com) monitors accidents at rock concerts.In their database, they list the names and other variables of victims whose deaths were
Costs To help travelers know what to expect, researchers collected the prices of commodities in 16 cities throughout the world. Here are boxplots comparing the prices of a ride on public

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