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Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions
The Valentine’s Day Lucky Lovers discount for couples averages $5.83 with a standard deviation of $8.62. We’ve seen that if the restaurant doubles the discount offer for two couples dining together on a single check, they can expect to save $11.66 with a standard deviation of $17.24. Some
On Valentine’s Day at the Quiet Nook, couples may get a Lucky Lovers discount averaging $5.83 with a standard deviation of $8.62. When two couples dine together on a single check, the restaurant doubles the discount offer—$40 for the ace of hearts on the first card and $20 on the
On Valentine’s Day the Quiet Nook restaurant offers a Lucky Lovers Special that could save couples money on their romantic dinners. When the waiter brings the check, he’ll also bring the four aces from a deck of cards. He’ll shuffle them and lay them out face down on the table. The couple
Parts A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. The company prefers to use supplier A because only 1% of those connectors prove to be defective, but supplier A can deliver only 70% of the connectors needed. The
Dishwashers Dan’s Diner employs three dishwashers. Al washes 20% of the dishes and breaks only 2% of those he handles. Betty and Chuck each wash 40% of the dishes, and Betty breaks only 2% of hers, but Chuck breaks 4% of the dishes he washes. (He, of course, will need a new job soon. . . .) You
E-readers II Given the e-reader data presented in Exercise 52.a) If a randomly selected U.S. adult has an e-reader, what is the probability that he or she hasn’t read an e-book in the past year?b) Is it more or less likely that a randomly selected U.S.adult who does not own an e-reader would have
Absenteeism, part II At the company described in Exercise 51, what percent of the absent employees are on the night shift?
E-readers PewInternet reported in January of 2014 that 32% of U.S. adults own at least one e-reader, and that 28% of U.S. adults read at least one e-book in the previous year (and thus, presumably, owned an e-reader).Overall, 76% of U.S. adults read at least one book(electronic or otherwise) in the
Absenteeism A company’s records indicate that on any given day about 2% of their day-shift employees and 4%of the night-shift employees will miss work. Fifty percent of the employees work the day shift.a) Is absenteeism independent of shift worked? Explain.b) What percent of employees are absent
Graduation, part II What percent of students who graduate from the college in Exercise 48 attended a public high school?
Late luggage Remember Leah (Exercise 47)? Suppose you pick her up at the Denver airport, and her luggage is not there. What is the probability that Leah’s first flight was delayed?
Graduation A private college report contains these statistics:75% of incoming freshmen attended public schools.65% of public school students who enroll as freshmen eventually graduate.95% of other freshmen eventually graduate.a) Is there any evidence that a freshman’s chances to graduate may
Gender A poll conducted by Gallup classified respondents by sex and political party, as shown in the table.Is party affiliation independent of the respondents’ sex?Explain. Democrat Republican Independent Male 32 28 34 Female 41 25 26
Snoring After surveying 995 adults, 81.5% of whom were over 30, the National Sleep Foundation reported that 36.8% of all the adults snored. 32% of the respondents were snorers over the age of 30.a) What percent of the respondents were 30 or less and did not snore?b) Is snoring independent of age?
Phone service According to estimates from the federal government’s 2010 National Health Interview Survey, based on face-to-face interviews in 16,676 households, approximately 63.6% of U.S. adults have both a landline in their residence and a cell phone, 25.4% have only cell phone service but no
Pets, again The local animal shelter in Exercise 22 reported that it currently has 24 dogs and 18 cats available for adoption; 8 of the dogs and 6 of the cats are male. Are the species and sex of the animals independent?Explain.
On the road again According to Exercise 16, the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04.a) What’s the probability that someone who has traveled to Mexico has visited Canada too?b) Are traveling to Mexico and to Canada
Eligibility A university requires its biology majors to take a course called BioResearch. The prerequisite for this course is that students must have taken either a Statistics course or a computer course. By the time they are juniors, 59% of the Biology majors have taken Statistics, 29% have had a
Shirts The soccer team’s shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 5 medium, 8 large, and 11 extra-large shirts. You want a medium for you and one for your sister. Find the probability of each event described.a) The first
Batteries A junk box in your room contains eighteen old batteries, seven of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome.a) The first two you choose are both good.b) At least one of the first three works.c) The first four
Cards You are dealt a hand of three cards, one at a time.Find the probability of each of the following.a) The first heart you get is the third card dealt.b) Your cards are all hearts.c) You get no hearts.d) You have at least one ace.
Global survey, take 2 Look again at the table summarizing the Roper survey in Exercise 19.a) If we select a respondent at random, what’s the probability we choose a person from the United States who has done post-graduate study?b) Among the respondents who have done post-graduate study, what’s
Pets In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male.Find each of the following conditional probabilities if an animal is selected at random:a) The pet is male, given that it is a
Amenities A check of dorm rooms on a large college campus revealed that 37% had refrigerators, 53% had TVs, and 24% had both a TV and a refrigerator. What’s the probability that a randomly selected dorm room hasa) a refrigerator but no TV?b) a refrigerator or a TV, but not both?c) neither a
Homes Real estate ads suggest that 57% of homes for sale have garages, 52% have swimming pools, and 14% have both. What is the probability that a home for sale hasa) a pool or a garage?b) neither a pool nor a garage?c) a pool but no garage?
Online banking last time Given the probabilities in Exercise 12, what is the probability that a person is younger than 50 given that she uses online banking? Has the probability that she is younger than 50 increased or decreased with the additional information?
Facebook again Suppose that the information in Exercise 9 had been presented in the following way. Facebook reports that 70% of its users are from outside the United States.Of the U.S. users, two-thirds log on every day. Of the non-U.S. users, three-sevenths log on every day. Draw a tree for this
Facebook Facebook reports that 70% of its users are from outside the United States and that 50% of its users log on to Facebook every day. Suppose that 20% of its users are U.S. users who log on every day. Make a probability table. Why is a table better than a tree here?
Tires You bought a new set of four tires that were recalled because 4% of the tires are defective. What is the probability that at least one of your tires is defective?
Religion Census reports for a city indicate that 62%of residents classify themselves as Christian, 12%as Jewish, and 16% as members of other religions (Muslims, Buddhists, etc.). The remaining residents classify themselves as nonreligious. A polling organization seeking information about public
Voters Suppose that in your city 29% of the voters are registered as Democrats, 29% as Republicans, and 15%as members of other parties (Liberal, Right to Life, Green, etc.). Voters not aligned with any official party are termed “Independent.” You are conducting a poll by calling registered
Champion bowler A certain bowler can bowl a strike 85% of the time. If the bowls are independent, what’s the probability that shea) goes three consecutive frames without a strike?b) makes her first strike in the third frame?c) has at least one strike in the first three frames?d) bowls a perfect
Dice You roll a fair die three times. What is the probability thata) you roll all 2’s?b) you roll all even numbers?c) none of your rolls gets a number divisible by 2?d) you roll at least one 6?e) the numbers you roll are not all 6’s?
Disjoint or independent? In Exercise 40, you calculated probabilities involving various blood types. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the
Disjoint or independent? In Exercise 39, you calculated probabilities of getting various M&M’s. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the events
Blood The American Red Cross says that about 45%of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB.a) Someone volunteers to give blood. What is the probability that this donor 1. has Type AB blood?2. has Type A or Type B?3. is not Type O?b) Among four potential
Polling, part II According to Pew Research, the contact rate (probability of contacting a selected household) was 90% in 1997 and 62% in 2012. However, the cooperation rate (probability of someone at the contacted household agreeing to be interviewed) was 43% in 1997 and dropped to 14% in 2012.a)
Polling As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 62% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 43% in 1997 to 14% in
Fathers, revisited Consider again the results of the poll about fathering discussed in Exercise 34. If we select two people at random from this sample,a) what is the probability that both think that being a father is easier today?b) what is the probability that neither thinks being a father is
More energy Exercise 33 shows the results of a Gallup Poll about energy. Suppose we select three people at random from this sample.a) What is the probability that all three responded“Develop wind and solar”?b) What is the probability that none responded “Equally important”?c) What
Failing fathers? A Pew Research poll in 2011 asked 2005 U.S. adults whether being a father today is harder than it was a generation ago. Here’s how they responded:If we select a respondent at random from this sample of 2005 adults,a) what is the probability that the selected person responded
Energy shortage Suppose a poll of 949 adults asked how to deal with an energy shortage: use more production, more conservation, or both? Here are the results:If we select a person at random from this sample of 949 adults,a) what is the probability that the person responded “More production”?b)
Final project You used the Multiplication Rule to calculate probabilities about the Calculus background of your Statistics groupmates in Exercise 30.a) What must be true about the groups in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
Repairs again You used the Multiplication Rule to calculate repair probabilities for your cars in Exercise 29.a) What must be true about your cars in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
Another project You are assigned to be part of a group of three students from the Intro Stats class described in Exercise 28. What is the probability that of your other two groupmates,a) neither has studied Calculus?b) both have studied at least one semester of Calculus?c) at least one has had more
More repairs Consider again the auto repair rates described in Exercise 27. If you own two cars, what is the probability thata) neither will need repair?b) both will need repair?c) at least one car will need repair?
Car repairs A consumer organization estimates that over a 1-year period 15% of cars will need to be repaired only once, 7% will need repairs exactly twice, and 1% will require three or more repairs. What is the probability that a car chosen at random will needa) no repairs?b) no more than one
College admissions II In Exercise 25, we saw that in 2013 Harvard accepted about 5.8% of its applicants, Dartmouth 10%, and Penn 12.1%. Jorge has applied to all three. He figures that his chances of getting into at least one of the three must be about 27.9%.a) How has he arrived at this
College admissions For high school students graduating in 2013, college admissions to the nation’s most selective schools were the most competitive in memory. Harvard accepted about 5.8% of its applicants, Dartmouth 10%, and Penn 12.1%. Jorge has applied to all three. Assuming that he’s a
Speeders Traffic checks on a certain section of highway suggest that 60% of drivers are speeding there. Since 0.6 * 0.6 = 0.36, the Multiplication Rule might suggest that there’s a 36% chance that two vehicles in a row are both speeding. What’s wrong with that reasoning?
Spinner The plastic arrow on a spinner for a child’s game stops rotating to point at a color that will determine what happens next. Which of the following probability assignments are legitimate? Probabilities of ... Red Yellow Green Blue a) 0.1 0.4 1.3 -1.8 b) 1 0 0 0 c) 0.25 0.25 0.25 0.25 d)
Jackpot On February 11, 2009, the AP news wire released the following story: (LAS VEGAS, Nev.)—A man in town to watch the NCAA basketball tournament hit a $38.7 million jackpot on Friday, the biggest slot machine payout ever. The 25-year-old software engineer from Los Angeles, whose name was not
Auto insurance Insurance companies collect annual payments from drivers in exchange for paying for the cost of accidents.a) Why should you be reluctant to accept a $1500 payment from your neighbor to cover his automobile accidents in the next year?b) Why can the insurance company make that offer?
Crash Commercial airplanes have an excellent safety record. Nevertheless, there are crashes occasionally, with the loss of many lives. In the weeks following a crash, airlines often report a drop in the number of passengers, probably because people are afraid to risk flying.a) A travel agent
Cold streak A basketball player missed 8 of 11 shots in the final portion of a game. When talking to reporters afterward, he says that he’s not worried about his next game because he’s due to make a lot of shots. Comment on his reasoning.
Winter Comment on the following quotation:“What I think is our best determination is it will be a colder than normal winter,” said Pamela Naber Knox, a Wisconsin state climatologist. “I’m basing that on a couple of different things. First, in looking at the past few winters, there has been
Sample spaces For each of the following, list the sample space and tell whether you think the events are equally likely:a) Toss 2 coins; record the order of heads and tails.b) A family has 2 children; record the number of boys.c) Flip a coin until you get a head or 4 consecutive tails.d) Roll three
Cell phones and surveys II The survey by the National Center for Health Statistics further found that 49% of adults ages 25–29 had only a cell phone and no landline.We randomly select four 25–29-year-olds:a) What is the probability that all of these adults have a only a cell phone and no
Cell phones and surveys A 2010 study conducted by the National Center for Health Statistics found that 25% of U.S. households had no landline service. This raises concerns about the accuracy of certain surveys, as they depend on random-digit dialing to households via landlines. We are going to pick
Playlists Your list of favorite songs contains 10 rock songs, 7 rap songs, and 3 country songs.a) What is the probability that a randomly played song is a rap song?b) What is the probability that a randomly played song is not country?
If P(green) = 0.35, what’s the probability the light isn’t green when you get to College and Main?
Does the coin “owe” you some tails? Suppose you spend that coin and your friend gets it in change. When she starts flipping the coin, should she expect a run of tails?
Age and party 2011 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
Pay According to the Bureau of Labor Statistics, the mean hourly wage for Chief Executives in 2009 was $80.43 and the median hourly wage was $77.27. By contrast, for General and Operations Managers, the mean hourly wage was $53.15 and the median was $44.55. Are these wage distributions likely to
Age and party 2011 The Pew Research Center conducts surveys regularly asking respondents which political party they identify with or lean toward. Among their results is the following table relating preferred political party and age. (people-press.org)a) What percent of people surveyed were
In 2007, pet food contamination put cats at risk, as well as dogs. Our experiment should probably test the safety of the new food on both animals.Questions: Why shouldn’t we randomly assign a mix of cats and dogs to the two treatment groups? What would you recommend instead?
Par 4 In theory, a golfer playing a par-4 hole tees off, hitting the ball in the fairway, then hits an approach shot onto the green. The first putt (usually long) probably won’t go in, but the second putt (usually much shorter)should. Sounds simple enough, but how many strokes might it really
Security There are 20 first-class passengers and 120 coach passengers scheduled on a flight. In addition to the usual security screening, 10% of the passengers will be subjected to a more complete search.a) Describe a sampling strategy to randomly select those to be searched.b) Here is the
NBA draft lottery Professional basketball teams hold a “draft” each year in which they get to pick the best available college and high school players. In an effort to promote competition, teams with the worst records get to pick first, theoretically allowing them to add better players. To
Acupuncture Research reported in 2008 brings to light the effectiveness of treating chronic lower back pain with different methods. One-third of nearly 1200 volunteers were administered conventional treatment (drugs, physical therapy, and exercise). The remaining patients got 30-minute acupuncture
Bias? Political analyst Michael Barone has written that“conservatives are more likely than others to refuse to respond to polls, particularly those polls taken by media outlets that conservatives consider biased” (Source: The Weekly Standard, March 10, 1997). The Pew Research Foundation tested
Age and party 2008 The Pew Research Center collected data from national exits polls conducted by NBC News after the 2008 presidential election. The following table shows information regarding voter age and party preference:a) What sampling strategy do you think the pollsters used? Explain.b) What
Pubs In England, a Leeds University researcher said that the local watering hole’s welcoming atmosphere helps men get rid of the stresses of modern life and is vital for their psychological well-being. Author of the report, Dr. Colin Gill, said rather than complain, women should encourage men to
Youthful appearance Readers’ Digest (April 2002, p. 168) reported results of several surveys that asked graduate students to examine photographs of men and women and try to guess their ages. Researchers compared these guesses with the number of times the people in the pictures reported having
Homecoming A college Statistics class conducted a survey concerning community attitudes about the college’s large homecoming celebration. That survey drew its sample in the following manner: Telephone numbers were generated at random by selecting one of the local telephone exchanges (first three
Laundry An experiment to test a new laundry detergent, SparkleKleen, is being conducted by a consumer advocate group. They would like to compare its performance with that of a laboratory standard detergent they have used in previous experiments. They can stain 16 swatches of cloth with 2 tsp of a
Tips, take 2 In another experiment to see if getting candy after a meal would induce customers to leave a bigger tip, a waitress randomly decided what to do with 80 dining parties. Some parties received no candy, some just one piece, and some two pieces. Others initially got just one piece of
Tips In restaurants, servers rely on tips as a major source of income. Does serving candy after the meal produce larger tips? To find out, two waiters determined randomly whether or not to give candy to 92 dining parties. They recorded the sizes of the tips and reported that guests getting candy
The lottery Many people spend a lot of money trying to win huge jackpots in state lotteries. Let’s play a simplified version using only the numbers from 1 to 20.You bet on three numbers. The state picks five winning numbers. If your three are all among the winners, you are rich!a) Simulate
Does the use of computer software in Introductory Statistics classes lead to better understanding of the concepts? A professor teaching two sections of Statistics decides to investigate. She teaches both sections using the same lectures and assignments, but gives one class statistics software to
Older Americans with a college education are significantly more likely to be emotionally well-off than are people in this age group with less education. Among those aged 65 and older, 35% scored 90 or above on the Emotional Health Index, but for those with a college degree, the percentage rose to
A soft-drink manufacturer must be sure the bottle caps on the soda are fully sealed and will not come off easily.Inspectors pull a few bottles off the production line at regular intervals and test the caps. If they detect any problems, they will stop the bottling process to adjust or repair the
An orange-juice processing plant will accept a shipment of fruit only after several hundred oranges selected from various locations within the truck are carefully inspected. If too many show signs of unsuitability for juice (bruised, rotten, unripe, etc.), the whole truckload is rejected. What
People aged 50 to 71 were initially contacted in the mid-1990s to participate in a study about smoking and bladder cancer. Data were collected from more than 280,000 men and 186,000 women from eight states who answered questions about their health, smoking history, alcohol intake, diet, physical
Tests of gene therapy on laboratory rats have raised hopes of stopping the degeneration of tissue that characterizes chronic heart failure. Researchers at the University of California, San Diego, used hamsters with cardiac disease, randomly assigning 30 to receive the gene therapy and leaving the
An artisan wants to create pottery that has the appearance of age. He prepares several samples of clay with four different glazes and test fires them in a kiln at three different temperature settings. What design? Analyze the design of each research example reported. Is it a sample survey, an
Widely used antidepressants may reduce ominous brain plaques associated with Alzheimer’s disease. In the study, mice genetically engineered to have large amounts of brain plaque were given a class of antidepressants that boost serotonin in the brain. After a single dose, the plaque levels
Some doctors have expressed concern that men who have vasectomies seemed more likely to develop prostate cancer. Medical researchers used a national cancer registry to identify 923 men who had had prostate cancer and 1224 men of similar ages who had not. Roughly one quarter of the men in each group
Does keeping a child’s lunch in an insulated bag, even with ice packs, protect the food from warming to temperatures where germs can proliferate? Researchers used an electric temperature gun on 235 lunches at preschools 90 minutes before they were to be eaten.Of the lunches with ice packs, over
People who read the last page of a mystery novel first generally like stories better. Researchers recruited 819 college students to read short stories, and for one story, they were given a spoiler paragraph beforehand. On the second and third story, the spoiler was incorporated as the opening
Fireworks manufacturers face a dilemma. They must be sure that the rockets work properly, but test-firing a rocket essentially destroys it. On the other hand, not testing the product leaves open the danger that they sell a bunch of duds, leading to unhappy customers and loss of future sales. The
In the journal Science, a research team reported that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years indicate that flowering has advanced an average of 15 days per decade, an indication of climate
Data were collected over a decade from 1021 men and women with a recent history of precancerous colon polyps.Participants were randomly assigned to receive folic acid(a B vitamin) or a placebo, and the study concluded that those receiving the folic acid may actually increase their risk of
The radioactive gas radon, found in some homes, poses a health risk to residents. To assess the level of contamination in their area, a county health department wants to test a few homes. If the risk seems high, they will publicize the results to emphasize the need for home testing. Officials plan
Researchers at the Purina Pet Institute studied Labrador retrievers for evidence of a relationship between diet and longevity. At 8 weeks of age, 2 puppies of the same sex and weight were randomly assigned to one of two groups—a total of 48 dogs in all. One group was allowed to eat all they
The journal Circulation reported that among 1900 people who had heart attacks, those who drank an average of 19 cups of tea a week were 44% more likely than nondrinkers to survive at least 3 years after the attack. What design? Analyze the design of each research example reported. Is it a sample
Researchers identified 242 children in the Cleveland area who had been born prematurely (at about 29 weeks).They examined these children at age 8 and again at age 20, comparing them to another group of 233 children not born prematurely. Their report, published in the New England Journal of
Skydiving, anyone? A humor piece published in the British Medical Journal (“Parachute use to prevent death and major trauma related to gravitational challenge:Systematic review of randomized control trials,”Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can’t tell for sure whether
Washing clothes A consumer group wants to test the effectiveness of a new “organic” laundry detergent and make recommendations to customers about how to best use the product. They intentionally stain 30 white T-shirts with grass in order to see how well the detergent will clean them. They want
Safety switch An industrial machine requires an emergency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experiment to find out whether workers will be able to deactivate the machine as quickly with their left hands as with their right hands. Be
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