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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
Stocks. Since the stock market began in 1872, stock prices have risen in about 73% of the years. Assuming that market performance is independent from year to year, what s the probability thata) the market will rise for 3 consecutive years?b) the market will rise 3 years out of the next 5?c) the
Beanstalks. In some cities tall people who want to meet and socialize with other tall people can join Beanstalk Clubs. To qualify, a man must be over 6'2"tall, and a woman over 5'10". According to the National Health Survey, heights of adults may have a Normal model with mean heights of 69.1" for
Play again. If you land in a penalty zone on the game board described in Exercise 12, your move will be determined by subtracting the roll of the die from the result on the spinner. Now what are the mean and standard deviation of the number of spots you may move?
Language. Neurological research has shown that in about 80% of people, language abilities reside in the brain s left side. Another 10% display right-brain language centers, and the remaining 10% have two-sided language control. (The latter two groups are mainly lefthanders; Science News, 161 no. 24
Child s play. In a board game you determine the number of spaces you may move by spinning a spinner and rolling a die. The spinner has three regions: Half of the spinner is marked 5, and the other half is equally divided between 10 and 20. The six faces of the die show 0, 0, 1, 2, 3, and 4 spots.
Twins, part III. At a large fertility clinic, 152 women became pregnant while taking Clomid. (See Exercise 7.)
At fault. The car insurance company in Exercise 8 believes that about 0.5% of drivers have an at-fault accident during a given year. Suppose the company insures 1355 drivers in that city.a) What are the mean and standard deviation of the number who may have at-fault accidents?b) Can you describe
More twins. A group of 5 women became pregnant while undergoing fertility treatments with the drug Clomid, discussed in Exercise 7. What s the probability thata) none will have twins?b) exactly 1 will have twins?c) at least 3 will have twins?
Deductible. A car owner may buy insurance that will pay the full price of repairing the car after an at-fault accident, or save $12 a year by getting a policy with a $500 deductible. Her insurance company says that about 0.5%of drivers in her area have an at-fault auto accident during any given
Twins. In the United States, the probability of having twins (usually about 1 in 90 births) rises to about 1 in 10 for women who have been taking the fertility drug Clomid. Among a group of 10 pregnant women, what s the probability thata) at least one will have twins if none were taking a fertility
Emergency switch. Safety engineers must determine whether industrial workers can operate a machine s emergency shutoff device. Among a group of test subjects, 66% were successful with their left hands, 82% with their right hands, and 51% with both hands.a) What percent of these workers could not
A game. To play a game, you must pay $5 for each play. There is a 10% chance you will win $5, a 40% chance you will win $7, and a 50% chance you will win only $3.a) What are the mean and standard deviation of your net winnings?b) You play twice. Assuming the plays are independent events, what are
Bipolar. Psychiatrists estimate that about 1 in 100 adults suffers from bipolar disorder. What s the probability that in a city of 10,000 there are more than 200 people with this condition? Be sure to verify that a Normal model can be used here?
Airfares. Each year a company must send 3 officials to a meeting in China and 5 officials to a meeting in France.Airline ticket prices vary from time to time, but the company purchases all tickets for a country at the same price.Past experience has shown that tickets to China have a mean price of
Workers. A company s human resources officer reports a breakdown of employees by job type and sex shown in the table.
Quality control. A consumer organization estimates that 29% of new cars have a cosmetic defect, such as a scratch or a dent, when they are delivered to car dealers.This same organization believes that 7% have a functional defect something that does not work properly and that 2% of new cars have
New bow, again. The archer in Exercise 46 continues shooting arrows, ending up with 45 bull s-eyes in 50 shots. Now are you convinced that the new bow is better?Explain.
Hotter hand. Our basketball player in Exercise 45 has new sneakers, which he thinks improve his game. Over his past 40 shots, he s made 32 much better than the 55% he usually shoots. Do you think his chances of making a shot really increased? In other words, is making at least 32 of 40 shots really
New bow. Our archer in Exercise 20 purchases a new bow, hoping that it will improve her success rate to more than 80% bull s-eyes. She is delighted when she first tests her new bow and hits 6 consecutive bull s-eyes. Do you think this is compelling evidence that the new bow is better? In other
Hot hand. A basketball player who ordinarily makes about 55% of his free throw shots has made 4 in a row. Is this evidence that he has a hot hand tonight? That is, is this streak so unusual that it means the probability he makes a shot must have changed? Explain.
True False. A true false test consists of 50 questions.How many does a student have to get right to convince you that he is not merely guessing? Explain.
ESP. Scientists wish to test the mind-reading ability of a person who claims to have ESP. They use five cards with different and distinctive symbols (square, circle, triangle, line, squiggle). Someone picks a card at random and thinks about the symbol. The mind reader must correctly identify which
Rickets. Vitamin D is essential for strong, healthy bones. Our bodies produce vitamin D naturally when sunlight falls upon the skin, or it can be taken as a dietary supplement. Although the bone disease rickets was largely eliminated in England during the 1950s, some people there are concerned that
Seatbelts II. Police estimate that 80% of drivers now wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use.a) How many cars do they expect to stop before finding a driver whose seatbelt is not buckled?b) What s the probability that the first unbelted driver
Earthquakes. Suppose the probability of a major earthquake on a given day is 1 out of 10,000.a) What s the expected number of major earthquakes in the next 1000 days?b) Use the Poisson model to approximate the probability that there will be at least one major earthquake in the next 1000 days.
TB again. In Chapter 15 we saw that the probability of contracting TB is small, with p about 0.0005 for a new case in a given year. In a town of 8000 peoplea) What s the expected number of new cases?b) Use the Poisson model to approximate the probability that there will be at least one new case of
Bank tellers. I am the only bank teller on duty at my local bank. I need to run out for 10 minutes, but I don t want to miss any customers. Suppose the arrival of customers can be modeled by a Poisson distribution with mean 2 customers per hour.a) What s the probability that no one will arrive in
Hurricanes, redux. We first looked at the occurrences of hurricanes in Chapter 4 (Exercise 41) and found that they arrive with a mean of 2.45 per year. Suppose the number of hurricanes can be modeled by a Poisson distribution with this mean.a) What s the probability of no hurricanes next year?b)
The euro. Shortly after the introduction of the euro coin in Belgium, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 140 heads that s 56% heads. Do you think this is evidence that
Annoying phone calls. A newly hired telemarketer is told he will probably make a sale on about 12% of his phone calls. The first week he called 200 people, but only made 10 sales. Should he suspect he was misled about the true success rate? Explain.
No-shows. An airline, believing that 5% of passengers fail to show up for flights, overbooks (sells more tickets than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 tickets. What s the probability the airline will not have enough seats, so someone gets bumped?
Lefties again. A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers.The average size of classes that meet there is 188, and we can assume that about 13% of students are left-handed.What s the probability that a right-handed student in one of these classes
Frogs, part II. Based on concerns raised by his preliminary research, the biologist in Exercise 28 decides to collect and examine 150 frogs.a) Assuming the frequency of the trait is still 1 in 8, determine the mean and standard deviation of the number of frogs with the trait he should expect to
Apples. An orchard owner knows that he ll have to use about 6% of the apples he harvests for cider because they will have bruises or blemishes. He expects a tree to produce about 300 apples.a) Describe an appropriate model for the number of cider apples that may come from that tree. Justify your
More arrows. The archer in Exercise 20 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 appropriate here? Explain.c) Use the 68 95 99.7 Rule to describe the distribution of the number of
And more tennis. Suppose the tennis player in Exercise 27 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 68 95
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 1 of every 8 frogs.He collects and examines a dozen frogs. If the frequency of the
Tennis, anyone? A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she serves 6 times, what s the probability she getsa) all 6 serves in?b) exactly 4 serves in?c) at least 4 serves in?d) no more than 4 serves in?
International students. At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. How many international students would you
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? With what standard deviation?
Still more arrows. Suppose our archer from Exercise 20 shoots 10 arrows.a) Find the mean and standard deviation of the number of bull s-eyes she may get.b) What s the probability that she never misses?c) What s the probability that there are no more than 8 bull s-eyes?d) What s the probability that
Still more lefties. Suppose we choose 12 people instead of the 5 chosen in Exercise 19.a) Find the mean and standard deviation of the number of right-handers in the group.b) What s the probability that they re not all righthanded?c) What s the probability that there are no more than 10 righties?d)
More arrows. Consider our archer from Exercise 20.a) How many bull s-eyes do you expect her to get?b) With what standard deviation?c) If she keeps shooting arrows until she hits the bull s-eye, how long do you expect it will take?
Lefties redux. Consider our group of 5 people from Exercise 19.a) How many lefties do you expect?b) With what standard deviation?c) If we keep picking people until we find a lefty, how long do you expect it will take?
Arrows. An Olympic archer is able to hit the bull s-eye 80% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what s the probability of each of the following results?a) Her first bull s-eye comes on the third arrow.b) She misses the bull s-eye at least once.c) Her
Lefties. Assume that 13% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below.a) The first lefty is the fifth person chosen.b) There are some lefties among the 5 people.c) The first lefty is the second or third person.d) There are exactly
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). If 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. If you spin a fair coin 100 times,a) Intuitively, how many heads do you expect?b) Use the formula for expected value to verify your intuition.
Colorblindness. About 8% of males are colorblind. A researcher needs some colorblind subjects for an experiment and begins checking potential subjects.a) On average, how many men should the researcher expect to check to find one who is colorblind?b) What s the probability that she won t find anyone
Blood. Only 4% of people have Type AB blood.a) On average, how many donors must be checked to find someone with Type AB blood?b) What s the probability that there is a Type AB donor among the first 5 people checked?c) What s the probability that the first Type AB donor will be found among the first
Cold calls. Justine works for an organization committed to raising money for Alzheimer s research. From past experience, the organization knows that about 20% of all potential donors will agree to give something if contacted by phone. They also know that of all people donating, about 5% will give
Customer center operator. Raaj works at the customer service call center of a major credit card bank.Cardholders call for a variety of reasons, but regardless of their reason for calling, if they hold a platinum card, Raaj is instructed to offer them a double-miles promotion.About 10% of all
Chips ahoy. For the computer chips described in Exercise 10, how many do you expect to test before finding a bad one?
More hoops. For the basketball player in Exercise 9, what s the expected number of shots until he misses?
Chips. Suppose a computer chip manufacturer rejects 2% of the chips produced because they fail presale testing.a) What s the probability that the fifth chip you test is the first bad one you find?b) What s the probability you find a bad one within the first 10 you examine?
Hoops. A basketball player has made 80% of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight s game hea) misses for the first time on his fifth attempt.b) makes his first basket on his fourth shot.c) makes his first basket on one of his first
Lost luggage. A Department of Transportation report about air travel found that airlines misplace about 5 bags per 1000 passengers. Suppose you are traveling 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?
On time. A Department of Transportation 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.b) Run at least 30 trials.c) Based on
Tiger again. Let s take one last look at the Tiger Woods picture search. You know his picture is in 20% of the cereal boxes. You buy five boxes to see how many pictures of Tiger you might get.a) Describe how you would simulate the number of pictures of Tiger you might find in five boxes of
Simulation II. You are one space short of winning a child s board game and must roll a 1 on a die to claim victory. You want to know how many rolls it might take.a) Describe how you would simulate rolling the die until you get a 1.b) Run at least 30 trials.c) Based on your simulation, estimate the
Simulating the model. Think about the Tiger Woods picture search again. You are opening boxes of cereal one at a time looking for his picture, which is in 20% of the boxes. You want to know how many boxes you might have to open in order to find Tiger.a) Describe how you would simulate the search
Bernoulli 2. Can we use probability models based on Bernoulli trials to investigate the following situations?Explain.a) You are rolling 5 dice and need to get at least two 6 s to win the game.b) We record the eye colors found in a group of 500 people.c) A manufacturer recalls a doll because about
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 the majority may have Type A blood, given that Type A is
Weightlifting. The Atlas BodyBuilding Company(ABC) sells starter sets of barbells that consist of one bar, two 20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard deviation of 0.25 pounds. The weights average the specified amounts, but the standard
Coffee and doughnuts. At a certain coffee shop, all the customers buy a cup of coffee; some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 320 cups and a standard deviation of 20 cups. He also believes that the number of
Bike sale. The bicycle shop in Exercise 44 will be offering 2 specially priced children s models at a sidewalk sale. The basic model will sell for $120 and the deluxe model for $150. Past experience indicates that sales of the basic model will have a mean of 5.4 bikes with a standard deviation of
Farmers market. A farmer has 100 lb of apples and 50 lb of potatoes for sale. The market price for apples(per pound) each day is a random variable with a mean of 0.5 dollars and a standard deviation of 0.2 dollars.Similarly, for a pound of potatoes, the mean price is 0.3 dollars and the standard
Bikes. Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take:The times for each setup phase are
Medley. In the medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted and creates a model based on the following assumptions:4 3 100a) What are the mean and standard
More pets. You re thinking about getting two dogs and a cat. Assume that annual veterinary expenses are independent and have a Normal model with the means and standard deviations described in Exercise 40.a) Define appropriate variables and express the total annual veterinary costs you may have.b)
More cereal. In Exercise 39 we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts in the boxes is a random variable with mean 16.2 ounces, and standard deviation 0.1 ounces.a) Find the expected amount of cereal left in the box.b) What s the
Pets. The American Veterinary Association claims that the annual cost of medical care for dogs averages $100, with a standard deviation of $30, and for cats averages$120, with a standard deviation of $35.a) What s the expected difference in the cost of medical care for dogs and cats?b) What s the
Cereal. The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.a) How much
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 5 times, what are the
Fire! An insurance company estimates that it should make an 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 annual
Donations. Organizers of a televised fund raiser 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 deviation
Tickets. A delivery company s trucks occasionally get parking tickets, and based on past experience, the company plans 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 18 should expect to hit on her way to work during a 5-day work week.
Repair calls. Find the mean and standard deviation of the number of repair calls the appliance shop in Exercise 17 should expect during an 8-hour day.
Garden. A company selling vegetable seeds in packets of 20 estimates that the mean number of seeds that will X1 1 X2 1 X3 X 2 5Y 0.2
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 3 dozen eggs without checking them.a) How many broken eggs do you expect to get?b) What s the standard deviation?c) What assumptions did you have to make
Random variables. Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of these variables:a)b) 3X c)d)e)
Random variables. Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of these variables:a) 0.8Y b)c)d)e)
Random variables. Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of these variables:a)b) 0.5Y c)d)e)
Random variables. Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of these variables:a) 3X b)c)d)e)
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)
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 your
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, and if it closes between 20 and 30 (inclusively), the option will be worth $200. A trader thinks there is a
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.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?b) What is the standard deviation?
Darts. Find the standard deviation of your winnings throwing darts in Exercise 8.
Kids again. Find the standard deviation of the number of children the couple in Exercise 7 may have.
The die. Find the standard deviation of the amount you might win rolling a die in Exercise 6.
Pick another card. Find the standard deviation of the amount you might win drawing a card in Exercise 5.
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