For a sales promotion, the manufacturer places winning symbols under the caps of 10% of all Pepsi bottles. You buy a six-pack. What is the probability that you win something?
> Return to the data on roller coasters seen in Exercise 23. Here is the distribution of the lengths of the rides of 241 coasters. We drew samples of 60 coasters from the full set of 241. We then repeated this 1000 times. For each sample, we found the mean
> An airline offers discounted advance-purchase fares to customers who buy tickets more than 30 days before travel and charges regular fares for tickets purchased during those last 30 days. The company has noticed that 60% of its customers take advantage o
> Police often set up sobriety check points roadblocks where drivers are asked a few brief questions to allow the officer to judge whether or not the person may have been drinking. If the officer does not suspect a problem, drivers are released to go on th
> Given the e-reader data presented in Exercise 52: 1. 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? 2. Is it more or less likely that a randomly selected U.S. adult who do
> At the company described in Exercise 51, what percent of the absent employees are on the night shift?
> Pew Internet 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
> A company records indicate that on any given day about 1% of their day-shift employees and 2% of the night-shift employees will miss work. Sixty percent of the employees work the day shift. 1. Is absenteeism independent of shift worked? Explain. 2. What
> What percent of students who graduate from the college in Exercise 48 attended a public high school?
> 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 first flight was delayed?
> A private college report contains these statistics: 70% of incoming freshmen attended public schools. 75% of public school students who enroll as freshmen eventually graduate. 90% of other freshmen eventually graduate. 1. Is there any evidence that a fre
> Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first fl
> Perhaps fans are just more interested in teams that win. The displays below are based on American League teams for the 2016 season. (Data in Attendance 2016) 1. Do winning teams generally enjoy greater attendance at their home games? Describe the associa
> A random survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. Is country of origin independent of type of driver?
> 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.
> 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. 1. What percent of the respondents were 30 or less and did not sno
> According to estimates from the federal government 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
> Given the table of probabilities from Exercise 24, are party affiliation and position on immigration independent? Explain.
> Given the table of probabilities from Exercise 23, are high blood pressure and high cholesterol independent? Explain.
> In Exercises 20 and 26, we looked at the birth orders and college choices of some Intro Stats students. For these students: 1. Are enrolling in Agriculture and Human Ecology disjoint? Explain. 2. Are enrolling in Agriculture and Human Ecology independent
> Early in 2010, Consumer Reports published the results of an extensive investigation of broiler chickens purchased from food stores in 23 states. Tests for bacteria in the meat showed that 62% of the chickens were contaminated with campylobacter, 14% with
> 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.
> If you draw a card at random from a well-shuffled deck, is getting an ace independent of the suit? Explain.
> American League baseball games are played under the designated hitter rule, meaning that pitchers, often weak hitters, do not come to bat. Baseball owners believe that the designated hitter rule means more runs scored, which in turn means higher attendan
> 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. 1. What the probability that someone who has traveled to Mexico has visited Canada too? 2. Are traveling to M
> A survey found that 73% of Americans have a home phone, 83% have a cell phone and 58% of people have both. 1. If a person has a home phone, what the probability that they have a cell phone also? 2. Are having a home phone and a cell phone independent eve
> Fifty-six percent of all American workers have a workplace retirement plan, 68% have health insurance, and 49% have both benefits. We select a worker at random. 1. What the probability he has neither employer-sponsored health insurance nor a retirement p
> 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, 52% of the biology majors have
> The soccer team shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extra-large shirts. You want a medium for you and one for your sister. Find the probability of e
> A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome. 1. The first two you choose are both good. 2. At least one of the fi
> You pick three cards at random from a deck. Find the probability of each event described below. 1. You get no aces. 2. You get all hearts. 3. The third card is your first red card. 4. You have at least one diamond.
> You are dealt a hand of three cards, one at a time. Find the probability of each of the following. 1. The first heart you get is the third card dealt. 2. Your cards are all red (that is, all diamonds or hearts). 3. You get no spades. 4. You have at least
> Twenty percent of cars that are inspected have faulty pollution control systems. The cost of repairing a pollution control system exceeds $100 about 40% of the time. When a driver takes her car in for inspection, what the probability that she will end up
> Seventy percent of kids who visit a doctor have a fever, and 30% of kids with a fever also have sore throats. What the probability that a kid who goes to the doctor has a fever and a sore throat?
> In the previous exercise you analyzed the association between the amounts of fat and sodium in fast food hamburgers. What about fat and calories? Here are data for the same burgers: a) Analyze the association between fat content and calories using correl
> Look again at the data about birth order of Intro Stats students and their choices of colleges shown in Exercise 20. 1. If we select a student at random, what the probability the person is an Arts and Sciences student who is a second child (or more)? 2.
> Look again at the table summarizing the Roper survey in Exercise 19. 1. a) If we select a respondent at random, what the probability we choose a person from the United States who has done post-graduate study? 2. Among the respondents who have done post-g
> The table shows the political affiliations of U.S. voters and their positions on supporting stronger immigration enforcement. 1. What the probability that 1. a randomly chosen voter favors stronger immigration enforcement? 2. a Republican favor
> The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table What the probability that 1. a man has both conditions? 2. a man has high blood pressure? 3. a man with high blood pressure has high chole
> 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
> You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities: 1. The card is a heart, given that it is red. 2. The card is red, given that it is a heart. 3. The card is an ace, given that it is red. 4.
> A survey of students in a large Introductory Statistics class asked about their birth order (1=oldest or only child) and which college of the university they were enrolled in. Here are the data: Suppose we select a student at random from this class. What
> The marketing research organization GfK Roper conducts a yearly survey on consumer attitudes worldwide. They collect demographic information on the roughly 1500 respondents from each country that they survey. Here is a table showing the number of people
> Employment data at a large company reveal that 72% of the workers are married, that 44% are college graduates, and that half of the college grads are married. What the probability that a randomly chosen worker 1. is neither married nor a college graduate
> A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TVs, and 21% had both a TV and a refrigerator. What the probability that a randomly selected dorm room has 1. a TV but no refrigerator? 2. a TV or a refrigerator
> Fast food is often considered unhealthy because much of it is high in both fat and sodium. But are the two related? Here are the fat and sodium contents of several brands of burgers. a) Analyze the association between fat content and sodium using correla
> Suppose 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. What the probability that an American chosen at random has 1. traveled to Canada but not Mexico? 2. traveled to either Canada o
> Recent research suggests that 73% of Americans have a home phone, 83% have a cell phone, and 58% of people have both. What is the probability that an American has 1. a home or cell phone? 2. neither a home phone nor a cell phone? 3. a cell phone but no h
> You shuffle a deck of cards and then start turning them over one at a time. The first one is red. So is the second. And the third. In fact, you are surprised to get 10 red cards in a row. You start thinking, The next one is due to be black! 1. Are you co
> On September 11, 2002, the first anniversary of the terrorist attack on the World Trade Center, the New York State Lottery daily number came up 9 11. An interesting coincidence or a cosmic sign? 1. What is the probability that the winning three numbers m
> You purchased a five-pack of new light bulbs that were recalled because 6% of the lights did not work. What is the probability that at least one of your lights is defective?
> 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 organizatio
> Suppose that in your city 37% of the voters are registered as Democrats, 29% as Republicans, and 11% as members of other parties (Liberal, Right to Life, Green, etc.). Voters not aligned with any official party are termed Independent. You are conducting
> To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he’ll get stopped on about 15% of work days. During a certain 5-day work week, what is the probability that he 1. g
> A certain bowler can bowl a strike 70% of the time. If the bowls are independent, what the probability that she 1. goes three consecutive frames without a strike? 2. makes her first strike in the third frame? 3. has at least one strike in the first three
> A survey was conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. The results are summarized in the following table. 1. Create a scatterplot. 2. What is the cor
> A slot machine has three wheels that spin independently. Each has 10 equally likely symbols: 4 bars, 3 lemons, 2 cherries, and a bell. If you play, what is the probability that 1. you get 3 lemons? 2. you get no fruit symbols? 3. you get 3 bells (the jac
> You roll a fair die three times. What is the probability that 1. you roll all 6? 2. you roll all odd numbers? 3. none of your rolls gets a number divisible by 3? 4. you roll at least one 5? 5. the numbers you roll are not all 5?
> 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 ass
> In Exercise 39, you calculated probabilities of getting various M&M. 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
> 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. 1. Someone volunteers to give blood. What is the probability that this donor 1. has Type AB blood? 2. has Type A or Type B?
> The Mars company says that before the introduction of purple, yellow candies made up 20% of their plain M&M, red another 20%, and orange, blue, and green each made up 10%. The rest were brown. 1. If you pick an M&M at random, what is the probability that
> 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
> 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 sur
> Consider again the results of the poll about fathering discussed in Exercise 34. If we select two people at random from this sample, 1. what is the probability that both think that being a father is easier today? 2. what is the probability that neither t
> Exercise 33 shows the results of a Gallup Poll about energy. Suppose we select three people at random from this sample. 1. What is the probability that all three responded Develop wind and solar? 2. What is the probability that none responded Equally imp
> Here are engine size (displacement, in liters) and gas mileage (estimated combined city and highway) for a random sample of 35 2016 model cars (taken from Fuel economy 2016 and identified in the data with Sample=Yes) 1. Make a scatterplot fo
> 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 how they responded: If we select a respondent at random from this sample of 2005 adults, 1. what is the probability that the sele
> A Gallup Poll (www.gallup.com/poll/161729/americans-divided-energy-environment-trade-off.aspx) in March 2013 asked 529 U.S. adults whether increasing oil, gas, and coal production or developing alternative energy sources such as wind and solar power shou
> You used the Multiplication Rule to calculate probabilities about the calculus background of your statistics groupmates in Exercise 30. 1. What must be true about the groups in order to make that approach valid? 2. Do you think this assumption is reasona
> You used the Multiplication Rule to calculate repair probabilities for your cars in Exercise 29. 1. What must be true about your cars in order to make that approach valid? 2. Do you think this assumption is reasonable? Explain.
> 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, 1. neither has studied calculus? 2. both have studied at least one semester of calcul
> Consider again the auto repair rates described in Exercise 27. If you own two cars, what is the probability that 1. neither will need repair? 2. both will need repair? 3. at least one car will need repair?
> In a large introductory statistics lecture hall, the professor reports that 55% of the students enrolled have never taken a calculus course, 32% have taken only one semester of calculus, and the rest have taken two or more semesters of calculus. The prof
> A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired only once, 7% will need repairs exactly twice, and 4% will require three or more repairs. What is the probability that a car chosen at random will need 1. no
> 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%. 1. How has he arr
> For high school students graduating in 2013, college admissions to the nation 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. Assumi
> Since 1985, average mortgage interest rates have fluctuated from a low of nearly 3% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that offered? Here is a scatterplot of Mortgage Loan Amount
> The following data relate traffic Density (measured as number of cars per mile) and the average Speed of traffic (in mph) on city highways. The data were collected at the same location at 10 different times randomly selected within a span of 3 months. 1.
> Although it hard to be definitive in classifying people as right- or left-handed, some studies suggest that about 14% of people are left-handed. Since 0.14—0.14=0.0196, the Multiplication Rule might suggest that there about a 2% chance that a brother and
> 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 a 36% chance that two vehicles in a row are both speeding. What wrong with that reasoning?
> Funding for many schools comes from taxes based on assessed values of local properties. People homes are assessed higher if they have extra features such as garages and swimming pools. Assessment records in a certain school district indicate that 37% of
> Suppose that 46% of families living in a certain county own a computer and 18% own an HDTV. The Addition Rule might suggest, then, that 64% of families own either a computer or an HDTV. What wrong with that reasoning?
> Many stores run secret sales : Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff (what is that?) only after the purchase has been totaled at the cash register. The store
> The plastic arrow on a spinner for a child game stops rotating to point at a color that will determine what happens next. Which of the following probability assignments are legitimate?
> 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 fr
> Insurance companies collect annual payments from drivers in exchange for paying for the cost of accidents. 1. Why should you be reluctant to accept a $1500 payment from your neighbor to cover his automobile accidents in the next year? 2. Why can the insu
> 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
> A basketball player missed 8 of 11 shots in the final portion of a game. When talking to reporters afterward, he says that he not worried about his next game because he due to make a lot of shots. Comment on his reasoning.
> The Office of Federal Housing Enterprise Oversight (www.fhfa.gov) collects data on various aspects of housing costs around the United States. Here is a scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states. The c
> After an unusually dry autumn, a radio announcer is heard to say, Watch out! We’ll pay for these sunny days later on this winter. Explain what he trying to say, and comment on the validity of his reasoning.
> 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
> The weather reporter on TV makes predictions such as a 25% chance of rain. What do you think is the meaning of such a phrase?
> A casino claims that its roulette wheel is truly random. What should that claim mean?
> 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 f
> 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
> 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
> Can special study courses actually help raise SAT scores? One organization says that the 30 students they tutored achieved an average gain of 60 points when they retook the test. 1. Explain why this does not necessarily prove that the special course caus
> Hoping to learn how to control crop damage by a certain species of beetle, a researcher plans to test two different pesticides in small plots of corn. A few days after application of the chemicals, he’ll check the number of beetle larvae found on each pl
> A research doctor has discovered a new ointment that she believes will be more effective than the current medication in the treatment of shingles (a painful skin rash). Eight patients have volunteered to participate in the initial trials of this ointment
> A polling organization is checking its database to see if the data sources it used sampled the same ZIP codes. The variable Datasource=1 if the data source is MetroMedia, 2 if the data source is DataQwest, and 3 if it RollingPoll. The organization finds
