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Statistics Concepts And Controversies 7th Edition David S Moore, William I Notz - Solutions

Mendel’s peas. Gregor Mendel used garden peas in some of the experiments that revealed that inheritance operates randomly. The seed color of Mendel’s peas can be either green or yellow. Suppose we produce seeds by“crossing” two plants, both of which carry the G (green) and Y (yellow)
Models legitimate and not. A bridge deck contains 52 cards, four of each of the 13 face values ace, king, queen, jack, ten, nine, . . . , two. You deal a single card from such a deck and record the face value of the card dealt. Give an assignment of probabilities to the possible outcomes that
An IQ test (optional). How high must a person score on the WAIS test to be in the top 10% of all scores? Use the information in Exercise III.14 and Table B to answer this question.
We like opinion polls (optional). Use the information in Exercise III.15 and Table B to find the probability that one sample misses the truth about the population by 4% or more. (This is the probability that the sample result is either less than 36% or greater than 44%.) (Hint: See pages 402–403.)
An IQ test (optional). Use the information in Exercise III.14 and Table B to find the probability that a randomly chosen person has aWAIS score 112 or higher.
We like opinion polls. Are Americans interested in opinion polls about the major issues of the day? Suppose that 40% of all adults are very interested in such polls. (According to sample surveys that ask this question, 40% is about right.) A polling firm chooses an SRS of 1015 people. If they do
An IQ test. TheWechsler Adult Intelligence Scale (WAIS) is a common IQ test for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 100 and standard deviation 15. Use the 68–95–99.7 rule to answer these questions.(a) What is the probability
Satisfaction with colleges. The National Center for Public Policy and Higher Education asked randomly chosen adults, “Are the colleges in your state doing an excellent, good, fair, or poor job, or don’t you know enough to say?” Assume that the results of the poll accurately reflect the
Choosing at random. Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm’s public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness, the choice will be made by drawing two names from a hat. (This is an SRS of size 2.)(a) Write down
Language study. Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results:Language: Spanish French German All others None Probability: 0.302 0.080 0.021 0.022 0.575(a) Explain why this is a legitimate probability
How much education? The 2008 Statistical Abstract gives this distribution of education for a randomly chosen American over 25 years old:Less than High school College, Associate’s Bachelor’s Advanced Education: high school graduate no bachelor’s degree degree degree Probability: 0.145 0.317
Poker. Deal a five-card poker hand from a shuffled deck. The probabilities of several types of hand are approximately as follows:Hand: Worthless One pair Two pairs Better hands Probability: 0.50 0.42 0.05 ?(a) What must be the probability of getting a hand better than two pairs? (Hint:See pages
Profit from a risky investment. Rotter Partners is planning a major investment. The amount of profit X is uncertain, but a probabilistic estimate gives the following distribution (in millions of dollars):Profit: 1 1.5 2 3 10 Probability: 0.3 0.2 0.2 0.2 0.1 What is the expected value of the profit?
Dice. What is the expected number of spots observed in rolling a carefully balanced die once? (Hint: See pages 429–432.)
Course grades. Choose a student at random from the course described in Exercise III.2 and observe what grade that student earns (A = 4, B = 3, C =2, D = 1, F = 0).(a) What is the expected grade of a randomly chosen student?(b) The expected grade is not one of the 5 grades possible for one student.
Blood types. People with Type B blood can receive blood donations from other people with either Type B or Type O blood. Tyra has Type B blood. What is the probability that 2 or more of Tyra’s 6 close friends can donate blood to her? Using your work in Exercise III.3, simulate 10 repetitions and
Course grades. If you choose 5 students at random from all those who have taken the course described in Exercise III.2, what is the probability that all the students chosen got a B or better? Simulate 10 repetitions of this random choosing and use your results to estimate the probability. (Your
Blood types. Choose a person at random and record his or her blood type. Here are the probabilities for each blood type:Blood type: Type O Type A Type B Type AB Probability: 0.4 0.3 0.2 ?(a) What must be the probability that a randomly chosen person has Type AB blood? (Hint: See pages
Course grades. Choose a student at random from all who took Math 101 in recent years. The probabilities for the student’s grade are Grade: A B C D F Probability: 0.2 0.4 0.2 0.1 ?(a) What must be the probability of getting an F?(b) To simulate the grades of randomly chosen students, how would you
What’s the probability? Open your local telephone directory to any page in the residential listing. Look at the last four digits of each telephone number, the digits that specify an individual number within an exchange given by the first three digits. Note the first of these four digits in each
Web-based exercise. The Web abounds in applets that simulate various random phenomena. One amusing probability problem is named Buffon’s needle. Draw lines 1 inch apart on a piece of paper, then drop a 1-inch-long needle on the paper. What is the probability that the needle crosses a line? You
Web-based exercise. The basketball player LeBron James makes about 70% of his free throws over an entire season. At the end of a game, an announcer states that “LeBron had a hot hand tonight. He made all 12 of his free throws.”Take LeBron’s probability of making a free throw to be 0.7 on each
The multiplication rule. Here is another basic rule of probability: if several events are independent, the probability that all of the events happen is the product of their individual probabilities.We know, for example, that a child has probability 0.49 of being a girl and probability 0.51 of being
The birthday problem. A famous example in probability theory shows that the probability that at least two people in a room have the same birthday is already greater than 1/2 when 23 people are in the room. The probability model is• The birth date of a randomly chosen person is equally likely to
More on the airport van. Let’s continue the simulation of Exercise 19.19. You have a backup van, but it serves several stations. The probability that it is available to go to the airport at any one time is 0.6. You want to know the probability that some passengers with reservations will be left
A multiple-choice exam. Matt has lots of experience taking multiplechoice exams without doing much studying. He is about to take a quiz that has 10 multiple-choice questions, each with four possible answers. Here is Matt’s personal probability model. He thinks that in 75% of questions he can
The airport van. Your company operates a van service from the airport to downtown hotels. Each van carries 7 passengers. Many passengers who reserve seats don’t show up—in fact, the probability is 0.25 that a randomly chosen passenger will fail to appear. Passengers are independent. If you
Playing craps. The game of craps is played with two dice. The player rolls both dice and wins immediately if the outcome (the sum of the faces) is 7 or 11. If the outcome is 2, 3, or 12, the player loses immediately. If he rolls any other outcome, he continues to throw the dice until he either wins
Two warning systems. An airliner has two independent automatic systems that sound a warning if there is terrain ahead (that means the airplane is about to fly into a mountain). Neither system is perfect. System A signals in time with probability 0.9. System B does so with probability 0.8. The
The Asian stochastic beetle. We can use simulation to examine the fate of populations of living creatures. Consider the Asian stochastic beetle.Females of this insect have the following pattern of reproduction:• 20% of females die without female offspring, 30% have 1 female offspring, and 50%
Gambling in ancient Rome. Tossing four astragali was the most popular game of chance in Roman times. Many throws of a present-day sheep’s astragalus show that the approximate probability distribution for the four sides of the bone that can land uppermost are Outcome Probability Narrow flat side
A better model for repeating an exam. A more realistic probability model for Elaine’s attempts to pass an exam in the previous exercise is as follows. On the first try she has probability 0.2 of passing. If she fails on the first try, her probability on the second try increases to 0.3 because she
Repeating an exam. Elaine is enrolled in a self-paced course that allows three attempts to pass an examination on the material. She does not study and has probability 2/10 of passing on any one attempt by luck. What is Elaine’s probability of passing in three attempts? (Assume the attempts are
Tonya’s free throws. Tonya makes 80% of her free throws in a long season. In a tournament game she shoots 5 free throws late in the game and misses 3 of them. The fans think she was nervous, but the misses may simply be chance. Let’s shed some light by estimating a probability.424 CHAPTER 19
LeBron’s free throws. The basketball player LeBron James makes about 70% of his free throws over an entire season. Take his probability of a success to be 0.7 on each shot. Using line 122 of Table A, simulate 25 repetitions of his performance in a game in which he shoots 10 free throws.(a)
More on class rank. In Exercise 19.8 you explained how to simulate the high school class rank of a randomly chosen college student. The Random Foundation decides to offer 8 randomly chosen students full college scholarships.What is the probability that no more than 3 of the 8 students chosen are in
More on course grades. In Exercise 19.7 you explained how to simulate the grade of a randomly chosen student in a statistics course. Five students on the same floor of a dormitory are taking this course. They don’t study together, so their grades are independent. Use simulation to estimate the
Class rank. Choose a college student at random and ask his or her class rank in high school. Probabilities for the outcomes are Top quarter but Top half but Bottom Class rank: Top 10% not top 10% not top quarter half Probability: 0.2 0.3 0.3 ?(a) What must be the probability that a randomly chosen
Course grades. Choose a student at random from all who took beginning statistics at Upper Wabash Tech in recent years. The probabilities for the student’s grade are Grade: A B C D or F Probability: 0.3 0.3 0.3 ?(a) What must be the probability of getting a D or an F?(b) To simulate the grades of
Simulating an opinion poll. A Gallup Poll on Presidents Day 2008 interviewed a random sample of 1007 adult Americans. Those in the sample were asked which former president they would like to bring back as the next president if they could. The poll showed that about 10% of adult Americans would
Basic simulation. Use Table A to simulate the responses of 10 independently chosen adults in each of the four situations of Exercise 19.3.(a) For situation (a), use line 110.(b) For situation (b), use line 111.(c) For situation (c), use line 112.(d) For situation (d), use line 113.
A small opinion poll. Suppose that 90% of a university’s students favor abolishing evening exams. You ask 10 students chosen at random. What is the probability that all 10 favor abolishing evening exams?(a) Give a probability model for asking 10 students independently of each other.(b) Assign
Which party does it better? An opinion poll selects adult Americans at random and asks them, “Which political party, Democratic or Republican, do you think is better able to manage the economy?” Explain carefully how you would assign digits from Table A to simulate the response of one person in
Selecting cards at random. In a standard deck of 52 cards, there are 13 spades, 13 hearts, 13 diamonds, and 13 clubs. Carry out a simulation to determine the probability that, when two cards are selected together at random from a standard deck, both have the same suit. Follow the steps given in
Selecting cards at random. In a standard deck of 52 cards, there are 13 spades, 13 hearts, 13 diamonds, and 13 clubs. How would you assign digits for a simulation to determine the suit (spades, hearts, diamonds, or clubs) of a card chosen at random from a standard deck of 52 cards?
Web-based exercise. One of the best ways to grasp the idea of probability is to watch the proportion of trials on which an outcome occurs gradually settle down at the outcome’s probability. Computer simulations can show this. Go to the Statistics: Concepts and Controversies Web site,
Web-based exercise. Search the Web to see if you can find an example of a misuse or misstatement of the law of averages. Explain why the statement you find is incorrect. (We found some examples by doing a Google search on the phrase “law of averages.”)
What probability doesn’t say. The probability of a head in tossing a coin is 1/2. This means that as we make more tosses, the proportion of heads will eventually get close to 0.5. It does not mean that the count of heads will get close to 1/2 the number of tosses. To see why, imagine that the
Reacting to risks. National newspapers such as USA Today and the New York Times carry many more stories about deaths from airplane crashes than about deaths from automobile crashes. Auto accidents killed about 45,000 people in the United States in 2006. Crashes of all scheduled air carriers,
Reacting to risks. The probability of dying if you play high school football is about 10 per million each year you play. The risk of getting cancer from asbestos if you attend a school in which asbestos is present for 10 years is about 5 per million. If we ban asbestos from schools, should we also
An unenlightened gambler.(a) A gambler knows that red and black are equally likely to occur on each spin 392 CHAPTER 17 Thinking about Chance of a roulette wheel. He observes five consecutive reds occur and bets heavily on black at the next spin. Asked why, he explains that black is “due by the
Snow coming. A meteorologist, predicting above-average snowfall this winter, says, “First, in looking at the past few winters, there has been belowaverage snowfall. Even though we are not supposed to use the law of averages, we are due.” Do you think that “due by the law of averages” makes
The “law of averages.” The baseball player Ichiro Suzuki gets a hit about 1/3 of the time over an entire season. After he has failed to hit safely in nine straight at-bats, the TV commentator says, “Ichiro is due for a hit by the law of averages.” Is that right? Why?
In the long run. Probability works not by compensating for imbalances but by overwhelming them. Suppose that the first 10 tosses of a coin give 10 tails and that tosses after that are exactly half heads and half tails. (Exact balance is unlikely, but the example illustrates how the first 10
Nash’s free throws. The basketball player Steve Nash is the all-time career free throw shooter among active players. He makes about 90% of his free throws. In today’s game, Nash misses his first two free throws. The TV commentator says, “Nash’s technique looks out of rhythm today.”
Surprising? You are getting to know your new roommate, assigned to you by the college. In the course of a long conversation, you find that both of you have sisters named Deborah. Should you be surprised? Explain your answer.
Playing Pick 4. The Pick 4 games in many state lotteries announce a four-digit winning number each day. The winning number is essentially a fourdigit group from a table of random digits. You win if your choice matches the winning digits, in exact order. The winnings are divided among all players
Personal random numbers? Ask several of your friends (at least 10 people) to choose a four-digit number “at random.” How many of the numbers chosen start with 1 or 2? How many start with 8 or 9? (There is strong evidence that people in general tend to choose numbers starting with low digits.)
Personal probability? When there are few data, we often fall back on personal probability. There had been just 24 space shuttle launches, all successful, before the Challenger disaster in January 1986. The shuttle program management thought the chances of such a failure were only 1 in 100,000.(a)
Personal probability versus data. Give an example in which you would rely on a probability found as a long-term proportion from data on many trials. Give an example in which you would rely on your own personal probability.
Marital status. The probability that a randomly chosen 50-yearold woman is divorced is about 0.18. This probability is a long-run proportion based on all the millions of women aged 50. Let’s suppose that the proportion stays at 0.18 for the next 30 years. Bridget is now 20 years old and is not
Will you have an accident? The probability that a randomly chosen driver will be involved in an accident in the next year is about 0.2. This is based on the proportion of millions of drivers who have accidents. “Accident”includes things like crumpling a fender in your own driveway, not just
Winning a baseball game. Over the period from 1967 to 2007 the champions of baseball’s two major leagues won 62% of their home games during the regular season. At the end of each season, the two league champions meet in the baseball World Series. Would you use the results from the regular season
From words to probabilities. Probability is a measure of how likely an event is to occur. Match one of the probabilities that follow with each statement of likelihood given. (The probability is usually a more exact measure of likelihood than is the verbal statement.)0 0.01 0.3 0.6 0.99 1(a) This
Two pairs. You read in a book on poker that the probability of being dealt two pairs in a five-card poker hand is 1/21. Explain in simple language what this means.
Tossing a thumbtack. Toss a thumbtack on a hard surface 100 times.How many times did it land with the point up? What is the approximate probability of landing point up?
How many tosses to get a head? When we toss a penny, experience shows that the probability (long-term proportion) of a head is close to 1/2. Suppose now that we toss the penny repeatedly until we get a head. What is the probability that the first head comes up in an odd number of tosses (1, 3, 5,
Random digits. The table of random digits (Table A) was produced by a random mechanism that gives each digit probability 0.1 of being a 0. What proportion of the first 200 digits in the table are 0s? This proportion is an estimate, based on 200 repetitions, of the true probability, which in this
Pennies falling over. You may feel that it is obvious that the probability of a head in tossing a coin is about 1/2 because the coin has two faces. Such opinions are not always correct. The previous exercise asked you to spin a penny rather than toss it—that changes the probability of a head. Now
Pennies spinning. Hold a penny upright on its edge under your forefinger on a hard surface, then snap it with your other forefinger so that it spins for some time before falling. Based on 50 spins, estimate the probability of heads.
Coin tossing and the law of averages. The author C. S. Lewis once wrote the following, referring to the law of averages: “If you tossed a coin a billion times, you could predict a nearly equal number of heads and tails.” Is this a correct statement of the law of averages? If not, how would you
Coin tossing and randomness. Toss a coin 10 times and record heads (H) or tails (T) on each toss. Which of these outcomes is most probable? Least probable?HTHTTHHTHT TTTTTHHHHH HHHHHHHHHH
Web-based exercise. Information about basketball players can be found at www.basketball-reference.com. Go to this Web site and find the percentage of three-point shots that Steve Nash has made in his career.(Nash is among the career leaders in percentage of three-point shots made.) On average, how
Web-based exercise. Most states have a lotto game that offers large prizes for choosing (say) 6 out of 51 numbers. If your state has a lotto game, find out what percentage of the money bet is returned to the bettors in the form of prizes. You should be able to find this information on the Web. What
Casino winnings. What is a secret, at least to naive gamblers, is that in the real world a casino does much better than expected values suggest. In fact, casinos keep a bit over 20% of the money gamblers spend on roulette chips.That’s because players who win keep on playing. Think of a player who
A common expected value. Here is a common setting that we simulated in Chapter 19: there are a fixed number of independent trials with the same two outcomes and the same probabilities on each trial. Tossing a coin, shooting basketball free throws, and observing the sex of newborn babies are all
Repeating an exam. Exercise 19.14 (page 424) gives a model for up to three attempts at an exam in a self-paced course. In that exercise, you simulated 50 repetitions to estimate Elaine’s probability of passing the exam. Use those simulations (or do 50 new repetitions) to estimate the expected
A multiple-choice exam. Charlene takes a quiz with 10 multiplechoice questions, each with four answer choices. If she just guesses independently at each question, she has probability 0.25 of guessing right on each. Use simulation to estimate Charlene’s expected number of correct answers.
Play this game, please. OK, friends, we’ve got a little deal for you.We have a fair coin (heads and tails each have probability 1/2). Toss it twice.If two heads come up, you win right there. If you get any result other than two heads, we’ll give you another chance: toss the coin twice more, and
We really want a girl. Example 4 estimates the expected number of children a couple will have if they keep going until they get a girl or until they have three children. Suppose that they set no limit on the number of children but just keep going until they get a girl. Their expected number of
Course grades. The distribution of grades in a large statistics course is as follows:Grade: A B C D F Probability: 0.2 0.3 0.3 0.1 0.1 To calculate student grade point averages, grades are expressed in a numerical scale with A = 4, B = 3, and so on down to F = 0.(a) Find the expected value. This is
Family size. The Census Bureau gives this distribution for the number of people in American families in 2006:Family size: 2 3 4 5 6 7 Proportion: 0.45 0.23 0.19 0.09 0.03 0.02 Chapter 20 Exercises 441(Note: In this table, 7 actually represents families of size 7 or greater. But for purposes of this
Life insurance. You might sell insurance to a 21-year-old friend. The probability that a man aged 21 will die in the next year is about 0.0015. You decide to charge $250 for a policy that will pay $100,000 if your friend dies.(a) What is your expected profit on this policy?(b) Although you expect
The Asian stochastic beetle again. In Exercise 20.12 you found the expected number of female offspring of the Asian stochastic beetle. Simulate the offspring of 100 beetles and find the mean number of offspring for these 100 beetles. Compare this mean with the expected value from Exercise
An expected rip-off? A “psychic” runs the following ad in a magazine:Expecting a baby? Renowned psychic will tell you the sex of the unborn child from any photograph of the mother. Cost, $20. Money-back guarantee.This may be a profitable con game. Suppose that the psychic simply
The Asian stochastic beetle. We met this insect in Exercise 19.16(page 425). Females have this probability model for their number of female offspring:Offspring: 0 1 2 Probability: 0.2 0.3 0.5(a) What is the expected number of female offspring?(b) Use the law of large numbers to explain why the
Rolling two dice. Example 2 of Chapter 18 (page 398) gives a probability model for rolling two casino dice and recording the number of spots on each of the two up-faces. That example also shows how to find the probability that the total number of spots showing is 5. Follow that method to give a
Keno. Keno is a popular game in casinos. Balls numbered 1 to 80 are tumbled in a machine as the bets are placed, then 20 of the balls are chosen at random. Players select numbers by marking a card. Here are two of the simpler Keno bets. Give the expected winnings for each.(a) A $1 bet on “Mark 1
Estimating sales. Gain Communications sells aircraft communications units. Next year’s sales depend on market conditions that cannot be predicted exactly. Gain follows the modern practice of using probability estimates of sales.The sales manager estimates next year’s sales as follows:Units
Making decisions. A six-sided die has two green and four red faces and is balanced so that each face is equally likely to come up. You must choose one of the following three sequences of colors:RGRRR RGRRRG GRRRRR Now start rolling the die. You will win $25 if the first rolls give the sequence you
Making decisions. The psychologist Amos Tversky did many studies of our perception of chance behavior. In its obituary of Tversky, the New York Times cited the following example.(a) Tversky asked subjects to choose between two public health programs that affect 600 people. One has probability 1/2
More roulette. An American roulette wheel has 38 slots, of which 18 are black, 18 are red, and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. Gamblers bet on roulette by placing chips on a table that lays out the numbers and colors of the 38
More Pick 4. Just as with Pick 3 (Example 2), you can make more elaborate bets in Pick 4. In the $1 StraightBox (24-way) bet, if you choose 1234 you win $2604 if the randomly chosen winning number is 1234 and you win $104 if the winning number has the digits 1, 2, 3, and 4 in any other order. What
Pick 4. The Tri-State Daily Numbers Pick 4 is much like the Pick 3 game of Example 1.Winning numbers for both are reported on television and in local newspapers. You pay $0.50 and pick a four-digit number. The state chooses a four-digit number at random and pays you $2500 if your number is
The numbers racket. Pick 3 lotteries (Example 1) copy the numbers racket, an illegal gambling operation common in the poorer areas of large cities.States usually justify their lotteries by donating a portion of the proceeds to education.One version of a numbers racket operation works as follows.
Kobe Bryant’s three-point shooting. Kobe Bryant makes about 1/3 of the three-point shots that he attempts. On average, how many three-point shots must he take in a game before he makes his first shot? In other words, we want the expected number of shots he takes before he makes his first.
Number of children. The Census Bureau gives this distribution for the number of a family’s own children under the age of 18 in American families in 2006:Number of children: 0 1 2 3 4 Proportion: 0.53 0.20 0.18 0.07 0.02 In this table, 4 actually represents 4 or more. But for purposes of this
Web-based exercise. You can compare the behavior of the mean and median by using the Mean and Median applet at the Statistics: Concepts and ControversiesWeb site, www.whfreeman.com/scc. Click to enter data, then use the mouse to drag an outlier up and watch the mean chase after it.
Web-based exercise. Willie Mays is fourth on the career home run list, behind Barry Bonds, Hank Aaron, and Babe Ruth. You can find Willie Mays’s home run statistics at the Web site www.baseball-reference.com. Construct four side-by-side boxplots comparing the yearly home run production of Barry
What graph to draw? We now understand three kinds of graphs to display distributions of quantitative variables: histograms, stemplots, and boxplots.Give an example (just words, no data) of a situation in which you would prefer each kind of graph.Notes and Data Sources 263 EXPLORING THE WEB

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