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inferential statistics
Stats Modeling The World AP Edition Grades 9-12 3rd Edition David E. Bock, Paul F. Velleman, Richard D. De Veaux - Solutions
Variation 2. Find the standard deviations of the random variables in Exercise 2.
Variation 1. Find the standard deviations of the random variables in Exercise 1.
Racehorse. A man buys a racehorse for $20,000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races, its value will jump to $100,000. If it wins one of the races, it will be worth $50,000. If it loses both races, it will be worth
Software. A small software company bids on two contracts. It anticipates a profit of $50,000 if it gets the larger contract and a profit of $20,000 on the smaller contract. The company estimates there s a 30% chance it will get the larger contract and a 60% chance it will get the smaller contract.
Carnival. A carnival game offers a $100 cash prize for anyone who can break a balloon by throwing a dart at it.It costs $5 to play, and you re willing to spend up to $20 trying to win. You estimate that you have about a 10% chance of hitting the balloon on any throw.a) Create a probability model
Kids. A couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys. (Assume boys and girls are equally likely.)a) Create a probability model for the number of children they ll have.b) Find the expected number of
You bet! You roll a die. If it comes up a 6, you win$100. If not, you get to roll again. If you get a 6 the second time, you win $50. If not, you lose.a) Create a probability model for the amount you win at this game.b) Find the expected amount you ll win.c) How much would you be willing to pay to
Pick a card, any card. You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $20 for the ace of clubs.a) Create a probability model for the amount you win at this game.b) Find the expected amount you ll win.c)
Stock market. A day trader buys an option on a stock that will return $100 profit if the stock goes up today and loses $200 if it goes down. If the trader thinks there is a 75% chance that the stock will go up, what is his expected value of the option?
Spinning the wheel. A wheel comes up green 50% of the time and red 50% of the time. If it comes up green, you win $100. If it comes up red, you win nothing.a) Intuitively, how much do you expect to win on one spin, on average?b) Calculate the expected value of the game.
Expected value. Find the expected value of each random variable:a) x 0 1 2 P(X = x) 0.2 0.4 0.4b) x 100 200 300 400 P(X = x) 0.1 0.2 0.5 0.2
Expected value. Find the expected value of each random variable:a) x 10 20 30 P(X = x) 0.3 0.5 0.2b) x 2 4 6 8 P(X = x) 0.3 0.4 0.2 0.1
Polygraphs. Lie detectors are controversial instruments, barred from use as evidence in many courts.Nonetheless, many employers use lie detector screening as part of their hiring process in the hope that they can avoid hiring people who might be dishonest. There has been some research, but no
HIV testing. In July 2005 the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of tests conducted were (correctly) positive, while for people without HIV 98.5% of the tests were(correctly)
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 40% of the dishes and breaks only 1% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 1% of hers, but Chuck breaks 3% of the dishes he washes. (He, of course, will need a new job soon. . . .) You go
No-shows. An airline offers discounted advancepurchase 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 of the advance-purchase fares. The
Drunks. Police often set up sobriety checkpoints 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 their way. Otherwise, drivers are
Lungs and smoke, again. Based on the statistics in Exercise 38, what s the probability that someone with the lung condition was a smoker?
Absenteeism, part II. At the company described in Exercise 37, what percent of the absent employees are on the night shift?
Lungs and smoke. Suppose that 23% of adults smoke cigarettes. It s known that 57% of smokers and 13% of nonsmokers develop a certain lung condition by age 60.a) Explain how these statistics indicate that lung condition and smoking are not independent.b) What s the probability that a randomly
Absenteeism. A company s 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.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 34 attended a public high school?
Late luggage. Remember Leah (Exercise 33)? 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:70% of incoming freshmen attended public schools.75% of public school students who enroll as freshmen eventually graduate.90% of other freshmen eventually graduate.a) Is there any evidence that a freshman s chances to graduate may
Luggage. 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 flight is delayed, the probability
Cars. 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 on the next page. Is country of origin independent of type of driver?
Montana. A 1992 poll conducted by the University of Montana classified respondents by sex and political party, as shown in the table. Is party affiliation independent of the respondents sex? Explain.
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 under 30 and did not snore?b) Is snoring independent of age?
Phone service. According to estimates from the federal government s 2003 National Health Interview Survey, based on face-to-face interviews in 16,677 households, approximately 58.2% of U.S. adults have both a landline in their residence and a cell phone, 2.8% have only cell phone service but no
Politics. Given the table of probabilities from Exercise 10, are party affiliation and position on the death penalty independent? Explain.
Men s health, again. Given the table of probabilities from Exercise 9, are high blood pressure and high cholesterol independent? Explain.
Birth order, finis. In Exercises 6 and 12 we looked at the birth orders and college choices of some Intro Stats students. For these students:a) Are enrolling in Agriculture and Human Ecology disjoint? Explain.b) Are enrolling in Agriculture and Human Ecology independent? Explain.c) Are being
Unsafe food. Early in 2007 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 81% of the chickens were contaminated with campylobacter, 15% with salmonella, and 13% with both.a)
Pets again. The local animal shelter in Exercise 8 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.
Cards. If you draw a card at random from a wellshuffled deck, is getting an ace independent of the suit?Explain.
On the road again. According to Exercise 2, 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
For sale. In the real-estate ads described in Exercise 1, 64% of homes for sale have garages, 21% have swimming pools, and 17% have both features.a) If a home for sale has a garage, what s the probability that it has a pool, too?b) Are having a garage and a pool independent events?Explain.c) Are
Benefits. 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.
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, 52% of the Biology majors have taken Statistics, 23% 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 4 medium, 10 large, and 6 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 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.a) The first two you choose are both good.b) At least one of the first three works.c) The first four
Another hand. You pick three cards at random from a deck. Find the probability of each event described below.a) You get no aces.b) You get all hearts.c) The third card is your first red card.d) You have at least one diamond.
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 red (that is, all diamonds or hearts).c) You get no spades.d) You have at least one ace.
Sick cars. 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 s the probability that she will end up paying more than $100 to repair
Sick kids. Seventy percent of kids who visit a doctor have a fever, and 30% of kids with a fever have sore throats. What s the probability that a kid who goes to the doctor has a fever and a sore throat?
Birth order, take 2. Look again at the data about birth order of Intro Stats students and their choices of colleges shown in Exercise 6.a) If we select a student at random, what s the probability the person is an Arts and Sciences student who is a second child (or more)?b) Among the Arts and
Global survey, take 2. Look again at the table summarizing the Roper survey in Exercise 5.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 postgraduate study, what s the
Death penalty. The table shows the political affiliations of American voters and their positions on the death penaltya) What s the probability that a randomly chosen voter favors the death penalty?b) What s the probability that a Republican favors the death penalty?c) What s the probability that a
Health. The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table:c) What s the probability that a man with high blood pressure has high cholesterol?d) What s the probability that a man has high blood pressure if it s known that he has high
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
Cards. You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities:a) The card is a heart, given that it is red.b) The card is red, given that it is a heart.c) The card is an ace, given that it is red.d) The card is a queen, given that it is a
Birth order. 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.a) What is the probability we select
Global survey. The marketing research organization GfK NOP 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 with various levels of
Workers. 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 s the probability that a randomly chosen workera) is neither married nor a college graduate?b) is married but not a college
Amenities. 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 s the probability that a randomly selected dorm room hasa) a TV but no refrigerator?b) a TV or a refrigerator, but not both?c) neither a TV nor
Travel. 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 s the probability that an American chosen at random hasa) traveled to Canada but not Mexico?b) traveled to either Canada or Mexico?c) not traveled to either
Homes. Real estate ads suggest that 64% of homes for sale have garages, 21% have swimming pools, and 17%have both features. 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?
Red cards. 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!a) Are you correct in thinking that there s a
9/11? On September 11, 2002, the first anniversary of the terrorist attack on the World Trade Center, the New York State Lottery s daily number came up 9 1 1.An interesting coincidence or a cosmic sign?a) What is the probability that the winning three numbers match the date on any given day?b) What
Pepsi. 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?
Tires. You bought a new set of four tires from a manufacturer who just announced a recall because 2% of those tires are defective. What is the probability that at least one of yours 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 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 a poll by calling
The train. 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 hea) gets stopped on Monday and again on
Champion bowler. A certain bowler can bowl a strike 70% of the time. What is 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 game (12 consecutive strikes)?
Slot machine. 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 thata) you get 3 lemons?b) you get no fruit symbols?c) you get 3 bells (the jackpot)?d) you get no bells?e) you
Dice. You roll a fair die three times. What is the probability thata) you roll all 6 s?b) you roll all odd numbers?c) none of your rolls gets a number divisible by 3?d) you roll at least one 5?e) the numbers you roll are not all 5 s?
Disjoint or independent? In Exercise 32 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 31 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
M&M s. The Masterfoods company says that before the introduction of purple, yellow candies made up 20% of their plain M&M s, red another 20%, and orange, blue, and green each made up 10%. The rest were brown.a) If you pick an M&M at random, what is the probability that 1) it is brown?2) it is
Polling, part II. According to Pew Research, the contact rate (probability of contacting a selected household) was 69% in 1997 and 76% in 2003. However, the cooperation rate (probability of someone at the contacted household agreeing to be interviewed) was 58% in 1997 and dropped to 38% in 2003.a)
Polling. As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers now can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey has fallen from 58% in 1997
Fathers revisited. Consider again the results of the poll about fathering discussed in Exercise 26. If we select two people at random from this sample,a) what is the probability that both think fathers are better today?b) what is the probability that neither thinks fathers are better today?c) what
More energy. Exercise 25 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 Protect the environment ?b) What is the probability that none responded Equally important ?c) What assumption did
Failing fathers? A Pew Research poll in 2007 asked 2020 U.S. adults whether fathers today were doing as good a job of fathering as fathers of 20 30 years ago.Here s how they responded:Response Number Increase production 342 Protect environment 583 Equally important 30 No opinion 50 Total 1005
Energy 2007. A Gallup poll in March 2007 asked 1005 U.S. adults whether increasing domestic energy production or protecting the environment should be given a higher priority. Here are the results:If we select a person at random from this sample of 1005 adults,a) what is the probability that the
Final project. You used the Multiplication Rule to calculate probabilities about the Calculus background of your Statistics groupmates in Exercise 22.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 21.a) What must be true about your cars in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
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 than one semester of Calculus?
Another project. You are assigned to be part of a group of three students from the Intro Stats class described in Exercise
More repairs. Consider again the auto repair rates described in Exercise 19. 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?
Stats projects. 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 professor randomly assigns
Car repairs. A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 7% will need repairs twice, and 4% 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 repair?c) some
College admissions II. In Exercise 17, we saw that in 2007 Harvard accepted about 9% of its applicants, Stanford 10%, and Penn 16%. Jorge has applied to all three.Assuming that he s a typical applicant, he figures that his chances of getting into at least one of the three must be about 35%.a) How
College admissions. For high school students graduating in 2007, college admissions to the nation s most selective schools were the most competitive in memory.(The New York Times, A Great Year for Ivy League Schools, but Not So Good for Applicants to Them, April 4, 2007). Harvard accepted about 9%
Lefties. Although it s hard to be definitive in classifying people as right or left handed, some studies suggest that about 14% of people are left handed. Since, the Multiplication Rule might suggest that there s about a 2% chance that a brother and a sister are both lefties. What s wrong with that
Speeders. Traffic checks on a certain section of highway suggest that 60% of drivers are speeding there. Since, 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?
Homes. Funding for many schools comes from taxes based on assessed values of local properties. People s 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 the residential properties have
Vehicles. Suppose that 46% of families living in a certain county own a car and 18% own an SUV. The Addition Rule might suggest, then, that 64% of families own either a car or an SUV. What s wrong with that reasoning?
Scratch off. 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 is required to reveal (in the
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 possible?
Jackpot. On January 20, 2000, the International Gaming Technology company issued a press release:(LAS VEGAS, Nev.) Cynthia Jay was smiling ear to ear as she walked into the news conference at The Desert Inn Resort in Las Vegas today, and well she should. Last night, the 37-year-old cocktail
Fire insurance. Insurance companies collect annual payments from homeowners in exchange for paying to rebuild houses that burn down.a) Why should you be reluctant to accept a $300 payment from your neighbor to replace his house should it burn down during the coming year?b) Why can the insurance
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 batter who had failed to get a hit in seven consecutive times at bat then hits a game-winning home run. When talking to reporters afterward, he says he was very confident that last time at bat because he knew he was due for a hit. Comment on his reasoning.
Snow. 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 s trying to say, and comment on the validity of 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 a lack of
Rain. 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?
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