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intro stats

Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions

Rainfall Statistics from Cornell’s Northeast Regional Climate Center indicate that Ithaca, New York, gets an average of 35.4 of rain each year, with a standard deviation of 4.2. Assume that a Normal model applies.a) During what percentage of years does Ithaca get more than 40 of rain?b) Less
Pregnancy Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days.a) What percentage of pregnancies should last between 270 and 280 days?b) At least how many days should the longest 25% of all pregnancies last?c) Suppose a
Safe cities Allstate Insurance Company identified the 10 safest and 10 least-safe U.S. cities from among the 200 largest cities in the United States, based on the mean number of years drivers went between automobile accidents.The cities on both lists were all smaller than the 10 largest cities.
Lucky spot? A reporter working on a story about the New York lottery contacted one of the authors of this book, wanting help analyzing data to see if some ticket sales outlets were more likely to produce winners. His data for each of the 966 New York lottery outlets are graphed below; the
Home values Assessment records indicate that the value of homes in a small city is skewed right, with a mean of$140,000 and standard deviation of $60,000. To check the accuracy of the assessment data, officials plan to conduct a detailed appraisal of 100 homes selected at random. Using the
GPAs A college’s data about the incoming freshmen indicates that the mean of their high school GPAs was 3.2, with a standard deviation of 0.30; the distribution was roughly mound-shaped and only slightly skewed.The students are randomly assigned to freshman writing seminars in groups of 25. What
CEOs, revisited In Exercise 42, you looked at the annual compensation for 800 CEOs, for which the true mean and standard deviation were (in thousands of dollars)10,307.31 and 17,964.62, respectively. A simulation drew samples of sizes 30, 50, 100, and 200 (with replacement)from the total annual
Waist size, revisited Researchers measured the Waist Sizes of 250 men in a study on body fat. The true mean and standard deviation of the Waist Sizes for the 250 men are 36.33 in and 4.019 inches, respectively.In Exercise 41, you looked at the histograms of simulations that drew samples of sizes 2,
CEO compensation The total compensation of the chief executive officers (CEOs) of the 800 largest U.S.companies (the Fortune 800) averaged (in thousands of dollars) 10,307.31 with a standard deviation (also in $1000) of 17,964.62. Here is a histogram of their annual compensations (in $1000):a)
Waist size A study measured the Waist Size of 250 men, finding a mean of 36.33 inches and a standard deviation of 4.02 inches. Here is a histogram of these measurements.a) Describe the histogram of Waist Size.b) To explore how the mean might vary from sample to sample, they simulated by drawing
Sampling, part II A sample is chosen randomly from a population that was strongly skewed to the left.a) Describe the sampling distribution model for the sample mean if the sample size is small.b) If we make the sample larger, what happens to the sampling distribution model’s shape, center, and
Sampling A sample is chosen randomly from a population that can be described by a Normal model.a) What’s the sampling distribution model for the sample mean? Describe shape, center, and spread.b) If we choose a larger sample, what’s the effect on this sampling distribution model?
Meals A restaurateur anticipates serving about 180 people on a Friday evening, and believes that about 20% of the patrons will order the chef’s steak special.How many of those meals should he plan on serving in order to be pretty sure of having enough steaks on hand to meet customer demand?
“No Children” section Some restaurant owners, at the request of some of their less tolerant customers, have stopped allowing children into their restaurant. This, naturally, outrages other customers. One restaurateur hopes to please both sets of customers by having a “no children” section.
Genetic defect It’s believed that 4% of children have a gene that may be linked to juvenile diabetes. Researchers hoping to track 20 of these children for several years test 732 newborns for the presence of this gene. What’s the probability that they find enough subjects for their study?
Gaydar Exercise 13 in Chapter 1 describes a study that showed that heterosexual women, during ovulation, were significantly better at correctly identifying the sexual orientation of a man from a photograph of his face than women who were not ovulating. In other words, ovulation improves a woman’s
Seeds Information on a packet of seeds claims that the germination rate is 92%. What’s the probability that more than 95% of the 160 seeds in the packet will germinate?Be sure to discuss your assumptions and check the conditions that support your model.
Polling Just before a referendum on a school budget, a local newspaper polls 364 voters in an attempt to predict whether the budget will pass. Suppose that the budget actually has the support of 52% of the voters. What’s the probability the newspaper’s sample will lead them to predict defeat?
Binge sample After hearing of the national result that 44% of students engage in binge drinking (5 drinks at a sitting for men, 4 for women), a professor surveyed a random sample of 244 students at his college and found that 96 of them admitted to binge drinking in the past week. Should he be
Back to school, again Based on the 72.2% national retention rate described in Exercise 29, does a college where 522 of the 603 freshmen returned the next year as sophomores have a right to brag that it has an unusually high retention rate? Explain.
Binge drinking As we learned in Chapter 14, a national study found that 44% of college students engage in binge drinking (5 drinks at a sitting for men, 4 for women). Use the 68–95–99.7 Rule to describe the sampling distribution model for the proportion of students in a randomly selected group
Back to school? 2013 Best known for its testing program, ACT, Inc., also compiles data on a variety of issues in education.In 2013, the company reported that the national college freshman-to-sophomore retention rate that had held steady at 74% over the previous several years had recently fallen
Contacts Assume that 30% of students at a university wear contact lenses.a) We randomly pick 100 students. Let pn represent the proportion of students in this sample who wear contacts.What’s the appropriate model for the distribution of pn? Specify the name of the distribution, the mean, and the
Loans Based on past experience, a bank believes that 11% of the people who receive loans will not make payments on time. The bank has recently approved 100 loans.a) What are the mean and standard deviation of the proportion of clients in this group who may not make timely payments?b) What
Mortgages 2013 In December, 2013, Lender Processing Services* reported that although mortgage defaults had fallen, in New York state, 12.4% of mortgages were still“noncurrent,” meaning that payments had been missed.Suppose a New York bank holds 1731 mortgages.a) Can you apply the Central Limit
Vision It is generally believed that nearsightedness affects about 14% of all children. A school district has registered 151 incoming kindergarten children.a) Can you apply the Central Limit Theorem to describe the sampling distribution model for the sample proportion of children who are
Smoking 2014 The Centers for Disease Control and Prevention estimated in 2014 that 18.1% of American adults smoked cigarettes. Using the 68–95–99.7 Rule, describe the sampling distribution model for the proportion of smokers among a randomly selected group of 60 adults.Be sure to discuss your
Speeding State police believe that 70% of the drivers traveling on a major interstate highway exceed the speed limit. They plan to set up a radar trap and check the speeds of 50 cars.a) Using the 68–95–99.7 Rule, draw and label the distribution of the proportion of these cars the police will
Too many green ones? In a really large bag of M&M’s, the students in Exercise 20 found 500 candies, and 12%of them were green. Is this an unusually large proportion of green M&M’s? Explain.
Just (un)lucky? One of the students in the introductory Statistics class in Exercise 19 claims to have tossed her coin 170 times and found only 43% heads. What do you think of this claim? Explain.
Bigger bag Suppose the class in Exercise 18 buys bigger bags of candy, with 200 M&M’s each. Again the students calculate the proportion of green candies they find.a) Explain why it’s appropriate to use a Normal model to describe the distribution of the proportion of green M&M’s they might
More coins Suppose the class in Exercise 17 repeats the coin-tossing experiment.a) The students toss the coins 25 times each. Use the 68–95–99.7 Rule to describe the sampling distribution model.b) Confirm that you can use a Normal model here.c) They increase the number of tosses to 64 each.
M&M’s The candy company claims that 10% of the M&M’s it produces are green. Suppose that the candies are packaged at random in small bags containing about 48 M&M’s. A class of elementary school students learning about percents opens several bags, counts the various colors of the candies, and
Coin tosses In a large class of introductory Statistics students, the professor has each student toss a coin 17 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions.a) What
More groceries Suppose the store in Exercise 14 had 312 customers this Sunday.a) Estimate the probability that the store’s revenues were at least $10,000.b) If, on a typical Sunday, the store serves 312 customers, how much does the store take in on the worst 10% of such days?
More tips The waiter in Exercise 13 usually waits on about 40 parties over a weekend of work.a) Estimate the probability that he will earn at least $500 in tips.b) How much does he earn on the best 10% of such weekends?
Groceries A grocery store’s receipts show that Sunday customer purchases have a skewed distribution with a mean of $32 and a standard deviation of $20.a) Explain why you cannot determine the probability that the next Sunday customer will spend at least $40.b) Can you estimate the probability that
Tips A waiter believes the distribution of his tips has a model that is slightly skewed to the right, with a mean of$9.60 and a standard deviation of $5.40.a) Explain why you cannot determine the probability that a given party will tip him at least $20.b) Can you estimate the probability that the
Market research II A market researcher for a provider of iPod accessories wants to know the proportion of customers who own cars to assess the market for a new iPod car charger. A survey of 600 customers indicates that 73% own cars.a) What is the standard deviation of the sampling distribution of
Market research A marketing researcher for a phone company surveys 178 people and finds that the proportion of customers who are likely to switch providers when their contract expires is 16%.a) What is the standard deviation of the sampling distribution of the proportion?b) If she wants to reduce
Soup A machine is supposed to fill cans with 16 oz of soup. Of course there, will be some variation in the amount actually dispensed, and measurement errors are often approximately normally distributed. The manager would like to understand the variability of the variances of the samples, so he
Sample maximum The distribution of scores on a Statistics test for a particular class is skewed to the left.The professor wants to predict the maximum score and so wants to understand the distribution of the sample maximum. She simulates the distribution of the maximum of the test for 30 different
Character recognition, again The automatic character recognition device discussed in Exercise 4 successfully reads about 85% of handwritten credit card applications.In Exercise 4, you looked at the histograms showing distributions of sample proportions from 1000 simulated samples of size 20, 50,
Send more money The philanthropic organization in Exercise 3 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 3, you looked at the histograms showing distribution of sample proportions from 1000 simulated mailings for samples of
Campus sample For her final project, Stacy plans on surveying a random sample of 60 students on whether they plan to go to Florida for Spring Break. From past years, she guesses that about 11% of the class goes.Is it reasonable for her to use a Normal model for the sampling distribution of the
Marriage According to a Pew Research survey, 27% of American adults are pessimistic about the future of marriage and the family. That is based on a random sample of about 1500 people. Is it reasonable for Pew Research to use a Normal model for the sampling distribution of the sample proportion? Why
Character recognition An automatic character recognition device can successfully read about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack of applications, the company did a simulation using samples of size 20, 50, 75, and 100. For each
Send money When they send out their fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for future appeals, they did a simulation using samples of size 20, 50,100, and 200.For each sample
Marketing The proportion of adult women in the United States is approximately 51%. A marketing survey telephones 400 people at random.a) What proportion of the sample of 400 would you expect to be women?b) What would the standard deviation of the sampling distribution be?c) How many women, on
Website An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via smartphones so they want to estimate the proportion of users who access the site that way (even if they also use their computers
A college physical education department asked a random sample of 200 female students to self-report their heights and weights, but the percentage of students with body mass indexes over 30 seemed suspiciously low. One possible explanation may be that the respondents “shaded” their weights down
Suppose that about 13% of the population is left-handed.10 A 200-seat school auditorium has been built with 15 “lefty seats,” seats that have the built-in desk on the left rather than the right arm of the chair. (For the right-handed readers among you, have you ever tried to take notes in a
The Centers for Disease Control and Prevention report that 22% of 18-year-old women in the United States have a body mass index (BMI)9 of 30 or more—a value considered by the National Heart, Lung, and Blood Institute to be associated with increased health risk As part of a routine health check at
According to the Centers for Disease Control and Prevention, about 18% of U.S.adults still smoke.Question: How much would we expect the proportion of smokers in a sample of size 1000 to vary from sample to sample?
Door prize You are among 100 people attending a charity fundraiser at which a large-screen TV will be given away as a door prize. To determine who wins, 99 white balls and 1 red ball have been placed in a box and thoroughly mixed. The guests will line up and, one at a time, pick a ball from the
Pregnant? Suppose that 70% of the women who suspect they may be pregnant and purchase an in-home pregnancy test are actually pregnant. Further suppose that the test is 98% accurate. What’s the probability that a woman whose test indicates that she is pregnant actually is?
Recalls In a car rental company’s fleet, 70% of the cars are American brands, 20% are Japanese, and the rest are German.The company notes that manufacturers’ recalls seem to affect 2% of the American cars, but only 1% of the others.a) What’s the probability that a randomly chosen car is
The Drake equation In 1961 astronomer Frank Drake developed an equation to try to estimate the number of extraterrestrial civilizations in our galaxy that might be able to communicate with us via radio transmissions.Now largely accepted by the scientific community, the Drake equation has helped
Coins A coin is to be tossed 36 times.a) What are the mean and standard deviation of the number of heads?b) Suppose the resulting number of heads is unusual, two standard deviations above the mean. How many“extra” heads were observed?c) If the coin were tossed 100 times, would you still
Socks In your sock drawer you have 4 blue socks, 5 gray socks, and 3 black ones. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability you end up wearinga) 2 blue socks.b) no gray socks.c) at least 1 black sock.d) a green sock.e) matching socks.
Volcanoes Almost every year, there is some incidence of volcanic activity on the island of Japan. In 2005 there were 5 volcanic episodes, defined as either eruptions or sizable seismic activity. Suppose the mean number of episodes is 2.4 per year. Let X be the number of episodes in the 2-year
O-rings Failures of O-rings on the space shuttle are fairly rare, but often disastrous, events. If we are testing O-rings, suppose that the probability of a failure of any one O-ring is 0.01. Let X be the number of failures in the next 10 O-rings tested.a) What model might you use to model X?b)
Dogs A census by the county dog control officer found that 18% of homes kept one dog as a pet, 4% had two dogs, and 1% had three or more. If a salesman visits two homes selected at random, what’s the probability he encountersa) no dogs?b) some dogs?c) dogs in each home?d) more than one dog in
Technology on campus Every 5 years the Conference Board of the Mathematical Sciences surveys college math departments. In 2000 the board reported that 51%of all undergraduates taking Calculus I were in classes that used graphing calculators and 31% were in classes that used computer assignments.
Plan B Here’s another attempt at developing a good strategy for the dice game in Exercise 33. Instead of stopping after a certain number of rolls, you could decide to stop when your score reaches a certain number of points.a) How many points would you expect a roll to add to your score?b) In
When to stop In Exercise 27 of the Review Exercises for Part III, we posed this question:You play a game that involves rolling a die. You can roll as many times as you want, and your score is the total for all the rolls. But … if you roll a 6, your score is 0 and your turn is over. What might be
Jerseys A Statistics professor comes home to find that all four of his children got white team shirts from soccer camp this year. He concludes that this year, unlike other years, the camp must not be using a variety of colors. But then he finds out that in each child’s age group there are 4
Who’s the boss? The 2013 State of Women-Owned Businesses Report commissioned by American Express(http://www.womenable.com/userfiles/downloads/2013 _State_of_Women-Owned_Businesses_Report_FINAL.pdf) says that, excluding large, publicly traded firms, women-owned firms make up 30% of the privately
Buying melons The first store in Exercise 28 sells watermelons for 32 cents a pound. The second store is having a sale on watermelons—only 25 cents a pound. Find the mean and standard deviation of the difference in the price you may pay for melons randomly selected at each store.
Home, sweet home According to the 2000 Census, 66%of U.S. households own the home they live in. A mayoral candidate conducts a survey of 820 randomly selected homes in your city and finds only 523 owned by the current residents. The candidate then attacks the incumbent mayor, saying that there is
Picking melons Two stores sell watermelons. At the first store the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store the melons are smaller, with a mean of 18 pounds and a standard deviation of 2 pounds. You select a melon at random at each store.a)
Travel to Kyrgyzstan Your pocket copy of Kyrgyzstan on 4237 { 360 Som a Day claims that you can expect to spend about 4237 som each day with a standard deviation of 360 som. How well can you estimate your expenses for the trip?a) Your budget allows you to spend 90,000 som. To the nearest day, how
Meals A college student on a seven-day meal plan reports that the amount of money he spends daily on food varies with a mean of $13.50 and a standard deviation of $7.a) What are the mean and standard deviation of the amount he might spend in two consecutive days?b) What assumption did you make in
Youth survey According to a recent Gallup survey, 93%of teens use the Internet, but there are differences in how teen boys and girls say they use computers. The telephone poll found that 77% of boys had played computer games in the past week, compared with 65% of girls. On the other hand, 76% of
Merger Explain why the facts you know about variances of independent random variables might encourage two small insurance companies to merge. (Hint: Think about the expected amount and potential variability in payouts for the separate and the merged companies.)
Teen smoking II Suppose that, as reported by the Centers for Disease Control, about 18% of high school students smoke tobacco. You randomly select 120 high school students to survey them on their attitudes toward scenes of smoking in the movies.a) What’s the expected number of smokers?b) What’s
Passing stats Molly’s college offers two sections of Statistics 101. From what she has heard about the two professors listed, Molly estimates that her chances of passing the course are 0.80 if she gets Professor Scedastic and 0.60 if she gets Professor Kurtosis.The registrar uses a lottery to
Teen smoking The Centers for Disease Control and Prevention say that about 18% of high-school students smoke tobacco (down from a high of 38% in 1997). Suppose you randomly select high-school students to survey them on their attitudes toward scenes of smoking in the movies. What’s the probability
Insurance A 65-year-old woman takes out a $100,000 term life insurance policy. The company charges an annual premium of $520. Estimate the company’s expected profit on such policies if mortality tables indicate that only 2.6% of women age 65 die within a year.
Stock strategy Many investment advisors argue that after stocks have declined in value for 2 consecutive years, people should invest heavily because the market rarely declines 3 years in a row.a) Since the stock market began in 1872, there have been two consecutive losing years eight times. In six
Multiple choice A multiple choice test has 50 questions, with 4 answer choices each. You must get at least 30 correct to pass the test, and the questions are very difficult.a) Are you likely to be able to pass by guessing on every question? Explain.b) Suppose, after studying for a while, you
Stocks Since the stock market began in 1872, stock prices have risen in about 73% of the years. Assuming that market performance is independent from year to year, what’s the probability thata) the market will rise for 3 consecutive years?b) the market will rise 3 years out of the next 5?c) the
Beanstalks In some cities tall people who want to meet and socialize with other tall people can join Beanstalk Clubs. To qualify, a man must be over 62 tall, and a woman over 510. According to the National Health Survey, heights of adults may have a Normal model with mean heights of 69.1 for
Play, again If you land in a “penalty zone” on the game board described in Exercise 12, your move will be determined by subtracting the roll of the die from the result on the spinner. Now what are the mean and standard deviation of the number of spots you may move?
Language Neurological research has shown that in about 80% of people, language abilities reside in the brain’s left side. Another 10% display right-brain language centers, and the remaining 10% have two-sided language control.(The latter two groups are mainly left-handers; Science News, 161 no.
Child’s play In a board game you determine the number of spaces you may move by spinning a spinner and rolling a die. The spinner has three regions: Half of the spinner is marked “5,” and the other half is equally divided between “10” and “20.” The six faces of the die show 0, 0, 1,
Twins, part III At a large fertility clinic, 152 women became pregnant while taking Clomid. (See Exercise 7.)a) What are the mean and standard deviation of the number of twin births we might expect?b) Can we use a Normal model in this situation? Explain.c) What’s the probability that no more than
At fault The car insurance company in Exercise 8 believes that about 0.5% of drivers have an at-fault accident during a given year. Suppose the company insures 1355 drivers in that city.a) What are the mean and standard deviation of the number who may have at-fault accidents?b) Can you describe the
More twins A group of 5 women became pregnant while undergoing fertility treatments with the drug Clomid, discussed in Exercise 7. What’s the probability thata) none will have twins?b) exactly 1 will have twins?c) at least 3 will have twins?
Deductible A car owner may buy insurance that will pay the full price of repairing the car after an at-fault accident, or save $12 a year by getting a policy with a$500 deductible. Her insurance company says that about 0.5% of drivers in her area have an at-fault auto accident during any given
Twins In the United States, the probability of having twins (usually about 1 in 90 births) rises to about 1 in 10 for women who have been taking the fertility drug Clomid.Among a group of 10 pregnant women, what’s the probability thata) at least one will have twins if none were taking a fertility
Emergency switch Safety engineers must determine whether industrial workers can operate a machine’s emergency shutoff device. Among a group of test subjects, 66% were successful with their left hands, 82% with their right hands, and 51% with both hands.a) What percent of these workers could not
A game To play a game, you must pay $5 for each play.There is a 10% chance you will win $5, a 40% chance you will win $7, and a 50% chance you will win only $3.a) What are the mean and standard deviation of your net winnings?b) You play twice. Assuming the plays are independent events, what are the
Bipolar Psychiatrists estimate that about 1 in 100 adults suffers from bipolar disorder. What’s the probability that in a city of 10,000 there are more than 200 people with this condition? Be sure to verify that a Normal model can be used here.
Airfares Each year a company must send 3 officials to a meeting in China and 5 officials to a meeting in France.Airline ticket prices vary from time to time, but the company purchases all tickets for a country at the same price.Past experience has shown that tickets to China have a mean price of
Workers A company’s human resources officer reports a breakdown of employees by job type and sex shown in the table.a) What’s the probability that a worker selected at random is i) female?ii) female or a production worker?iii) female, if the person works in production?iv) a production worker,
Quality control A consumer organization estimates that 29% of new cars have a cosmetic defect, such as a scratch or a dent, when they are delivered to car dealers. This same organization believes that 7% have a functional defect—something that does not work properly—and that 2% of new cars have
Quality control, part 2 The cell phone manufacturer in Exercise 60 wants to model the time between events.The mean number of defective cell phones is 2 per day.a) What model would you use to model the time between events?b) What would the probability be that the time to the next failure is 1 day or
Web visitors, part 2 The website manager in Exercise 59 wants to model the time between purchases. Recall that the mean number of purchases in the evening is 4 per minute.a) What model would you use to model the time between events?b) What is the mean time between purchases?c) What is the
Quality control In an effort to improve the quality of their cell phones, a manufacturing manager records the number of faulty phones in each day’s production run. The manager notices that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of

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