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intro stats

Stats Data And Models (Subscription) 3rd Edition Richard D De Veaux, Paul D Velleman, David E Bock - Solutions

Random variables. Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: a) X - 20 b) 0.5Y Mean SD c) X + Y d) X - Y X 80 12 e) Y + Y Y 12 3
Random variables. Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: a) 3X b) Y + 6 c) X + Y d) X - Y e) X + X XY Mean SD 10 20 25
Kittens. In a litter of seven kittens, three are female.You pick two kittens at random.a) Create a probability model for the number of male kittens you get.b) What’s the expected number of males?c) What’s the standard deviation?
Batteries. In a group of 10 batteries, 3 are dead. You choose 2 batteries at random.a) Create a probability model for the number of good batteries you get.b) What’s the expected number of good ones you get?c) What’s the standard deviation?
Contracts. Your company bids for two contracts. You believe the probability you get contract #1 is 0.8. If you get contract #1, the probability you also get contract #2 will be 0.2, and if you do not get #1, the probability you get#2 will be 0.3.a) Are the two contracts independent? Explain.b) Find
Contest. You play two games against the same opponent.The probability you win the first game is 0.4. If you win the first game, the probability you also win the second is 0.2. If you lose the first game, the probability that you win the second is 0.3.a) Are the two games independent? Explain.b)
Day trading. An option to buy a stock is priced at $200.If the stock closes above 30 on May 15, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30 (inclusively), the option will be worth $200. Atrader thinks there is a 50%
Cancelled flights. Mary is deciding whether to book the cheaper flight home from college after her final exams, but she’s unsure when her last exam will be. She thinks there is only a 20% chance that the exam will be scheduled after the last day she can get a seat on the cheaper flight. If it is
Insurance. An insurance policy costs $100 and will pay policyholders $10,000 if they suffer a major injury(resulting in hospitalization) or $3000 if they suffer a minor injury (resulting in lost time from work). The company estimates that each year 1 in every 2000 policyholders may have a major
Defects. A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc.). While none had more than three of these defects, 7% had three, 11% two, and 21%one defect. Find the expected number of appearance defects in a new car and the standard
Red lights. A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below.a) How many red lights should she expect to hit each day?b) What’s the standard
Repairs. The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour.a) How many calls should the shop expect per hour?b) What is the standard deviation? Repair Calls Probability 0 12 3 0.1 0.3 0.4 0.2
Darts. Find the standard deviation of your winnings throwing darts in Exercise 6.
Kids, again. Find the standard deviation of the number of children the couple in Exercise 5 may have.
The die. Find the standard deviation of the amount you might win rolling a die in Exercise 4.
Pick another card. Find the standard deviation of the amount you might win drawing a card in Exercise 3.
Find the standard deviations of the random variables in Exercise 2.
Variation
Find the standard deviations of the random variables in Exercise 1.
Variation
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 and knows it can only get one of them. 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%
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 might 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.b) Find the expected amount you’ll win.c) What would you be willing to pay to play this game?
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.b) Find the expected amount you’ll win.c) What would
Expected value. Find the expected value of each random variable: a) x 0 1 2 P(X = x) 0.2 0.4 0.4 b) 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 0.2 2 4 6 8 P(X = x) 0.3 0.4 0.2 0.1 b) x
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
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
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. Acompany’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. Is country of origin independent of type of driver? Origin Driver Student Staff American 107 105 European 33 12 Asian 55 47
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. Democrat Republican Independent Male 36 45 24 Female 48 33 16
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. Party Death Penalty Favor Oppose Republican 0.26 0.04 Democrat 0.12 0.24 Other 0.24 0.10
Men’s health, again. Given the table of probabilities from Exercise 9, are high blood pressure and high cholesterol independent? Explain. Cholesterol High OK Blood Pressure High OK 0.11 0.11 0.21 0.16 0.52
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.a) What’s the probability he has neither employersponsored health insurance nor a retirement plan?b) What’s the probability
Eligibility. Auniversity 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 extralarge 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
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?
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 Sciences students,
Birth order, take
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 probability the
Global survey, take
Death penalty. The table shows the political affiliations of American voters and their positions on the death penalty.a) What’s the probability that i) a randomly chosen voter favors the death penalty?ii) a Republican favors the death penalty?iii) a voter who favors the death penalty is a
Health. The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table.What’s the probability that:a) a man has both conditions?b) a man has high blood pressure?c) a man with high blood pressure has high cholesterol?d) a man has high blood
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 11 = oldest or only child2 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 is the probability that the
Global survey. 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 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
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
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
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. Apolling 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 registered
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
Champion bowler. A certain bowler can bowl a strike 70% of the time. 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 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
at least one person is Type B?
they are not all Type A?
no one is Type AB?
all are Type O?
is not Type O?b) Among four potential donors, what is the probability that
has Type A or Type B?
has Type AB blood?
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
at least one is green?
none are yellow?
the third one is the first one that’s red?
they are all brown?

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