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Stats Data And Models 3rd Canadian Edition Richard De Veaux, Paul Velleman, David Bock, Augustin Vukov, Augustine Wong - Solutions

More arrows Kateri Vrakking, the archer in Exercise 62, will be shooting 200 arrows in a large competition.a) What are the mean and standard deviation of the number of bull’s-eyes she might get?b) Is a Normal model an appropriate approximation here? Explain.c) Use the 68–95–99.7 Rule to
And more tennis Suppose the tennis player in Exercise 65 serves 80 times in a match.a) What are the mean and standard deviation of the number of good first serves expected?b) Verify that you can use a Normal model to approximate the distribution of the number of good first serves.c) Use the
Frogs A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in one of every eight frogs. He collects and examines a dozen frogs. If the frequency
Tennis, anyone? A particular tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she serves six times, what is the probability that she getsa) all six serves in?b) exactly four serves in?c) at least four serves in?d) no more than
International students At a certain university, 6% of all students come from outside Canada. Incoming students are assigned at random to freshman dorms, where they live in residential clusters of 40 freshmen sharing a common lounge area. How many international students would you expect to find in
Vision It is generally believed that nearsightedness affects about 12% of all children. A school district tests the vision of 169 incoming kindergarten children. How many would you expect to be nearsighted, on average? With what standard deviation?
Arrows Kateri Vrakking, an Olympic archer, is able to hit the bull’s-eye 80% of the time. Assume each shot is independent of the others. She shoots 10 arrows.a) Find the mean and standard deviation of the number of bull’s-eyes she may get.b) What is the probability that she never misses?c) What
Lefties Assume that 13% of people are left-handed. We select 12 people at random.a) Find the mean and standard deviation of the number of right-handers in the group.b) What is the probability that they’re not all right-handed?c) What is the probability that there are no more than 10 righties?d)
Roulette and intuition An American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green (0 and 00). You spin the wheel 38 times.a) Intuitively, how many times would you expect the ball to wind up in a green slot?b) Use the formula for expected value to verify your
Coins and intuition You flip a fair coin 100 times.a) Intuitively, how many heads do you expect?b) Use the formula for expected value to verify your intuition.
Lost luggage A Transport Canada report about air travel found that airlines misplace about 5 bags per 1000 passengers. Suppose you are travelling with a group of people who have checked 22 pieces of luggage on your flight. Can you consider the fate of these bags to be Bernoulli trials? Explain.
On time A Transport Canada report about air travel found that, nationwide, 76% of all flights are on time. Suppose you are at the airport and your flight is one of 50 scheduled to take off in the next two hours. Can you consider these departures to be Bernoulli trials? Explain.
Seatbelts Suppose 75% of all drivers always wear their seatbelts. Let’s investigate how many of the drivers might be belted among five cars waiting at a traffic light.a) Describe how you would simulate the number of seatbelt-wearing drivers among the five cars (for example, using random numbers,
De Grasse again Let’s take one last look at the De Grasse picture search. You know his picture is in 20% of the cereal boxes. You buy five boxes to see how many pictures of De Grasse you might get.a) Describe how you would simulate the number of pictures of De Grasse you might find in five boxes
Bernoulli 2 Can we use probability models based on Bernoulli trials to investigate the following situations? Explain.a) You are rolling five dice and need to get at least two 6s to win the game.b) We record the eye colours found in a group of 500 people.c) A manufacturer recalls a doll because
Bernoulli Can we use probability models based on Bernoulli trials to investigate the following situations? Explain.a) We roll 50 dice to find the distribution of the number of spots on the faces.b) How likely is it that in a group of 120 people the majority will have Type A blood, given that Type
Casino A casino knows that people play the slot machines in hopes of hitting the jackpot, but that most of them lose their dollar. Suppose a certain machine pays out an average of $0.92, with a standard deviation of $120.a) Why is the standard deviation so large?b) If you play five times, what are
Fire! An insurance company estimates that it should make an expected annual profit of $150 on each homeowner’s policy written, with a standard deviation of $6000.a) Why is the standard deviation so large?b) If it writes only two of these policies, what are the mean and standard deviation of the
Donations Organizers of a televised fundraiser know from past experience that most people donate small amounts ($10–$25), some donate larger amounts ($50–$100), and a few people make very generous donations of $250, $500, or more. Historically, pledges average about $32 with a standard
Tickets A delivery company’s trucks occasionally get parking tickets. Based on past experience, the company expects that the trucks will average 1.3 tickets a month, with a standard deviation of 0.7 tickets.a) If they have 18 trucks, what are the mean and standard deviation of the total number
Stop! Find the mean and standard deviation of the number of red lights the commuter in Exercise 32 will hit on her way to work during a five-day work week. State any assumptions you are making.
Repair calls Find the mean and standard deviation of the number of repair calls the appliance shop in Exercise 31 will receive during an 8-hour day. State any assumptions you are making.
Garden A company selling vegetable seeds in packets of 20 estimates that the mean number of seeds that will actually grow is 18, with a standard deviation of 1.2 seeds. You buy five different seed packets.a) What is your expected number of bad (non-growing) seeds?b) What is the standard deviation
Eggs A grocery supplier believes that in a dozen eggs, the mean number of broken ones is 0.6 with a standard deviation of 0.5 eggs. You buy three dozen eggs without checking them.a) What is your expected number of broken eggs?b) What is the standard deviation?c) What assumptions did you have to
Random variables fini Given independent random variables X and Y, with means and standard deviations as shown, find the mean and standard deviation of each of the variables below. X1 , X2 , and X3 are independent variables with the same distribution as X.a) 2Y + 20b) 3Xc) 0.25X + Yd) X − 5Ye) X1
Random variables III Given independent random variables X and Y, with means and standard deviations as shown, find the mean and standard deviation of each of the variables below. Also, Y1 , Y2 , Y3 , and Y4 are independent variables with the same distribution as Y.a) 0.8Yb) 2X − 100c) X + 2Yd)
Random variables II Given independent random variables X and Y, with means and standard deviations as shown, find the mean and standard deviation of each of the variables below. Also, Y1 and Y2 are independent variables with the same distribution as Y.a) X − 20b) 0.5Yc) X + Yd) X − Ye) Y1 + Y2
Random variables Given independent random variables X and Y, with means and standard deviations as shown, find the mean and standard deviation of each of the random variables below. Also, X1 and X2 are independent variables with the same distribution as X.a) 3Xb) Y + 6c) X + Yd) X − Ye) X1 + X2
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 is the expected number of males?c) What is the standard deviation?
Batteries In a group of 10 batteries, 3 are dead. You choose two batteries at random.a) Create a probability model for the number of good batteries you get.b) What is your expected number of good ones?c) What is the standard deviation?
Contracts Your company bids for two contracts. You believe the probability that you will get contract 1 is 0.8. If you get contract 1, the probability that you will also get contract 2 will be 0.2. If you do not get contract 1, the probability that you will get contract 2 will be 0.3.a) Are the two
Contest You play two games against the same opponent. The probability that you win the first game is 0.4. If you win the first game, the probability that 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?
Day trading again 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. If it closes between 20 and 30 (inclusively), the option will be worth $200. A trader thinks there is a 50%
Cancelled flights Mary is deciding whether to book the cheaper flight home from university 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
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% had two, and 21% had one defect. Find the expected number of appearance defects in a new car, and the
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. X = # of red 0 1 2 3 4 5 P(X = x) 0.05 0.25 0.35 0.15 0.15 0.05a) How many red
Repairs The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. Repair Calls 0 1 2 3 Probability 0.1 0.3 0.4 0.2a) How many calls should the shop expect per hour, on average?b) What is the standard deviation?
Darts Find the standard deviation of your winnings throwing darts in Exercise
Kids again Find the standard deviation of the number of children the couple in Exercise 21 may have.
The die Find the standard deviation of the amount you might win rolling a die in Exercise
Pick another card Find the standard deviation of the amount you might win drawing a card in Exercise
Variation 2 Find the standard deviations of the random variables in Exercise
Variation 1 Find the standard deviations of the random variables in Exercise
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 only
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 is 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 the cash prize. You estimate that you have about a 10% chance of hitting the balloon on any throw.a) Create a
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
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 per spin of the wheel, on average?b) Calculate the expected value of the game.
Expected value II Find the expected value of each random variable: a)
Expected value Find the expected value of each random variable:a) b) Chapter Exercises x 10 20 30 P(X = x) 0.3 0.5 0.2 x 100 200 300 400 P(X = x) 0.1 0.2 0.5 0.2 x 0 1 2 P(X = x) 0.2 0.4 0.4 x 2 4 6 8 P(X = x) 0.3 0.4 0.2 0.1 b)
Soccer again If this team has 200 corner kicks over the season, what are the chances that they score more than 22 times?
Toasters again In a batch of 10,000 toasters, what are the chances that fewer than 450 need to be returned?
Ketchup An automatic filling machine in a factory fills bottles of ketchup with a mean of 16.1 oz and a standard deviation of 0.05 oz with a distribution that can be well modelled by a Normal model. What is the probability that your bottle of ketchup contains less than 16 oz?
Battery The life span of a calculator battery is normally distributed with a mean of 45 hours and a standard deviation of 5 hours. What is the probability that a battery lasts more than 53 hours?
Passing on A large hospital has an average of 7 fatalities in a week. Using the Poisson model, what is the probability that this week has 10 fatalities
Sell! A car dealership sells an average of 5 cars in a day. Using the Poisson model, what is the probability that the dealer sells 3 cars tomorrow?
Soccer A soccer team estimates that they will score on 8% of the corner kicks. In next week’s game, the team hopes to kick 15 corner kicks. What are the chances that they will score on 2 of those opportunities?
Toasters A manufacturer ships toasters in cartons of 20.In each carton, they estimate a 5% chance that one of the toasters will need to be sent back for minor repairs. What is the probability that in a carton, there will be exactly 3 toasters that need repair?
Golf scores A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of 11.Assuming that the second nine has the same mean and standard deviation, what is the mean and standard deviation of his total score if he
Salary An employer’s total salary expenses for a 5-day workweek have a mean of $1250 with a standard deviation of $129. On the weekends, his total salary expenses have a mean of $450 with a standard deviation of $57. What is the mean and standard deviation of his total weekly salaries?
Caffeinated again What is the standard deviation for Exercise 2?
Oranges again What is the standard deviation for Exercise 1?
Caffeinated A coffee shop tracks sales and has observed the distribution shown in the following table. What is the average daily sales that it can expect? # of Sales 145 150 155 160 170 Probability 0.15 0.22 0.37 0.19 0.07
Oranges A citrus farmer has observed the following distribution for the number of oranges per tree. How many oranges does he expect on average? Oranges 25 30 35 40 Probability 0.10 0.40 0.30 0.20
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 Digby’s Diner employs three dishwashers. Alma washes 40% of the dishes and breaks only 1% of those she handles. Filip and Kai each wash 30% of the dishes. Filip breaks only 1% of the dishes he washes, but Kai breaks 3% of the dishes he washes. (He, of course, will need a new job soon.
Polygraphs Lie detectors are controversial instruments, barred from use as evidence in Canadian courts. Nonetheless, some 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
Drunks Police often set up impaired driving checkpoints—roadblocks where drivers are asked a few brief questions to allow the officer to judge whether 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, second puff Based on the statistics in Exercise 56, what is the probability that someone with the lung condition was a smoker?
Absenteeism, part II At the company described in Exercise 55, 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 is 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
Further postsecondary What percent of students who go on to university from the private high school in Exercise 52 attended a public primary school?
Late luggage Remember Leah from Exercise 51? Suppose you pick her up at the Vancouver airport and her luggage is not there. What is the probability that Leah’s first flight was delayed?
Postsecondary A private high school report contains these statistics: 70% of incoming Grade 9 students attended public primary schools. 75% of the students who came from public primary school go on to university after completing high school. 90% of the students who did not come from public primary
Luggage Leah is flying from Moncton to Vancouver with a connection in Montreal. The probability that 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 Montreal is 0.95, but if the first flight is delayed, the
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. Thirty-two percent 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
Television According to Statistics Canada, about 46% of the television we watch is Canadian programming on Canadian channels. (If this seems high to you, just think of news programs and hockey games.) Close to 15% of what we watch is foreign programming on foreign channels, and we don’t watch
Death Penalty, reborn Given the table of percentages from Exercise 34, are being a Conservative and favouring the death penalty independent events? Explain. In Favour of the Death Penalty (%) Not in Favour of the Death Penalty (%) Conservatives 31.2 8.8 Liberal 10.2 9.8 NDP 17.1 12.9 Bloc
Birth order, finis In Exercise 36, we looked at the birth orders and faculty choices of some Intro Stats students.a) Are enrolling in Agriculture and Human Ecology disjoint? Explain.b) Are enrolling in Agriculture and Human Ecology independent? Explain.c) Are being first-born and enrolling in Human
Cosmetic marketing again In Exercise 35, we looked at the results of a survey reported by GfK Roper Worldwide about cosmetic marketing Country Agree Disagree Don’t Know Total China 361 988 153 1502 France 695 763 81 1539 India 828 689 18 1535 UK 597 898 62 1557 US 668 841 48 1557 Total 3149 4179
Pets again The local animal shelter in Exercise 32 reported that it currently has 24 dogs and 18 cats available for adoption; eight of the dogs and six of the cats are male. Are the species and sex of the animals independent? (For example, are the events dog and male independent events?) Explain.
Cards III If you draw a card at random from a wellshuffled deck, is getting an ace independent of the suit? Explain.
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
Cards again 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 is 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 is the probability that a kid who goes to the doctor has a fever and a sore throat? What did you assume to answer this question?
Birth order A survey of students in a large Introductory Statistics class were asked about their birth order (1 = oldest or only child) and which faculty of the university they were studying under. Here are the data:a) If we select a student at random, what is the probability that the person is an
Cosmetic marketing A GfK Roper Worldwide survey asked consumers in five countries whether they agreed with the statement “I follow a skin care routine every day.” Here are the responses classified by the country of the respondent.Country Agree Disagree Don’t Know Total China 361 988 153 1502
Death Penalty The following table from a 2013 Angus Reid poll shows the political affiliation of Canadian voters and their positions on the death penalty (in percentage). In Favour of the Death Penalty (%) Not in Favour of the Death Penalty (%) Conservatives 31.2 8.8 Liberal 10.2 9.8 NDP 17.1 12.9
Men’s health The table shows the approximate probabilities that an adult Canadian male has high blood pressure and/or high cholesterol.Blood Pressure Cholesterol High OK High 0.11 0.21 OK 0.16 0.52a) What is the probability that a man has both conditions?b) What is the probability that he has
Pets In its monthly report, a local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and six 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
Craps The game of Craps starts with a player tossing a pair of dice. If dice add up to 2 or 3 or 12, the player’s turn is up and they “crap out.” You’re determined to win at this game.a) What is the probability that you crap out on your next turn?b) What is the probability that you crap out
Lottery tickets The Ontario Lottery Association claims that your odds of winning a prize on an Instant Win Crossword game are 1 in 3.09. This means that any ticket has probability 1>3.09 = 0.324 of winning a prize. Every Friday you buy one Crossword game.a) What is the probability you don’t win a
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?
Ottawa revisited Sixty percent of Ottawans drive their own vehicles to work, 7% ride as passengers in someone else’s vehicle, 22% take public transit, 10% walk or cycle, and the remainder get to work some other way. You are conducting a poll by calling Ottawans at random. In your first four

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