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essential statistics

Essential Statistics 1st Edition David S Moore - Solutions

12.22 Random stock prices. A believer in the random walk theory of stock markets thinks that an index of stock prices has probability 0.65 of increasing in any year. Moreover, the change in the index in any given year is not influenced by whether it rose or fell in earlier years. Let X be the
12.21 Testing ESP. In a test for ESP (extrasensory percep tion), a subject is told that cards the experimeiater but not the subject can see contain either a star, a circle, a wave, or a square.As the experimenter looks at each of 20 cards in turn, the sub ject names the shape on the card. A subject
12.20 Binomial setting? A binomial distribution will be ap proximately correct as a model for one of these two sports set tings and not for the other. Explain why by briefly discussing both settings.(a) A National Football League kicker has made 80% of his field goal attempts in the past. This
12.19 Binomial setting? In each situation below, is it reason able to use a binomial distribution for the random variable Xl Give reasons for your answer in each case.(a) An auto manufacturer chooses one car from each hour's production for a detailed quality inspection. One variable recorded is the
12.18 Ten lines in the tahle contain 400 digits. The count of Os in these lines is approximately Normal with(a) mean 40 and standard deviation 36.(b) mean 40 and standard deviation 6.(c) mean 36 and standard deviation 6.
12.17 The mean number of Os in a line 40 digits long is(a) 4. (b) 3.098. (c) 0.4.
12.16 The probability of finding exactly 4 Os in a line 40 digits long is about(a) 0.0000225. (b) 0.0225. (c) 0.2059.
12.15 A basketball player makes 70% of her free throws. She takes 7 free throws in a game. If the shots are independent of each other, the probability that she makes 5 out of the 7 shots is about(a) 0.635. (b) 0.318. (c) 0.015.Each entry in a table of random digits like Table B has probability 0.1
12.14 A basketball player makes 70% of her free throws. She takes 7 free throws in a game. If the shots are independent of each other, the probability tbat she makes the first 5 and misses the last 2 is about (a) 0.635. (b) 0.318. (c) 0.015.
12.13 In a group of 10 college students, 4 are business ma jors. You choose 3 of the 10 students at random and ask their major. The distribution of the number of business majors you choose is(a) binomial withn = 10 and p = 0.4.(b) binomial with n = 3 and p = 0.4.(c) not binomial.
12.12 Joe reads that 1 out of 4 eggs contains salmonella bac teria. So he never uses more than 3 eggs in cooking. If eggs do or don't contain salmonella independently of each other, the number of contaminated eggs when Joe uses 3 chosen at ran dom has the distribution(a) binomial with n = 4 and p =
12.11 Checking for survey errors. One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. About 12% of American adulrs are black. The num ber X of blacks in random samples of 1500
12.10 College admissions. A small liberal arts college would like to have an entering class of 415 students next year. Past experience shows that about 27% of the students admit ted will decide to attend. The college therefore plans to admit 1535 students. Suppose that students make their decisions
12.9 Using Benford's law. According to Benford's law (Example 9.6, page 171) the prob ability that the first digit of the amount of a randomly chosen invoice is a 1 or a 2 is 0.477. You examine 90 invoices from a vendor and find that 29 have first digits 1 or 2. If Benford's law holds, the count of
12.8 Random digit dialing. When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random digit dialing machine make 15 calls.(a) What is the mean number of calls that reach a person?(b) What is the standard deviation a of the
12.7 Proofreading. Return to the proofreading setting of Exercise 12.5.(a) If X is the number of word errors missed, what is the distribution of XI If Y is the number of word errors caught, what is the distribution of Y?(b) What is the mean number of errors caught? What is the mean number of errors
12.6 Random digit dialing. When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random digit dialing machine make 15 calls.(a) What is the probability that exactly 3 calls reach a person?(b) What is the probability that at most
12.5 Proofreading. Typing errors in a text are either nonword errors (as when "the" is typed as "teh") or word errors that result in a real but incorrect word. Spell-checking software will catch nonword errors but not word errors. Fluman proofreaders catch 70% of word errors. You ask a fellow
12.4 Teens feel the heat. Opinion polls find that 63% of American teens say that their parents put at least some pressure on them to get into a good college.' If you take an SRS of 1000 teens, what is the approximate distribution of the numbet in your sample who say they feel at least some pressure
12.3 Computer instruction. A student studies binomial distributions using computerassisted instruction. After the lesson, the computer presents 10 problems. The student solves each problem and enters her answer. The computer gives additional instruction between problems if the answer is wrong. The
12.2 Random digit dialing. When an opinion poll calls residential telephone num bers at random, only 20% of the calls reach a live persoia. You watch the ran dom dialing machine make calls. X is the number of calls until the first live person answers.
12.1 Random digit dialing. When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random dialing ma chine make 15 calls. X is the number that reach a live person.
11.52 Jasmine has alleles A and O. Tyrone has alleles B and O.(a) What is the probability that a child of these parents has blood type O?(b) If Jasmine and Tyrone have three children, what is the probability that all three have blood type O?(c) What is the probability that the first child has blood
11.51 Isabel has alleles A and O. Carlos has alleles A and B.They have two children.(a) What is the probability that both children have blood type A?(b) What is the probability that both children have the same blood type?
11.50 Sarah and David both have alleles B and O.(a) What blood types can their children have?(b) What is the probability that their next child has each of these blood types?
11.49 Rachel and Jonathan both have alleles A and B.(a) What blood types can their children have?(b) What is the probability that their next child has each of these blood types?
11.48 Fundraising by telephone. Tree diagrams can orga nize problems having more than two stages. Figure 11.6 shows probabilities for a charity calling potential donors by tele phone.'^ Each person called is either a recent doiaor, a past donor, or a new prospect. At the next stage, the person
11.47 Lactose intolerance. Lactose intolerance causes diffi culty digesting dairy products that contain lactose (milk sugar).It is particularly common among people of African and Asian ancestry. In the United States (ignoring other groups and peo ple who consider themselves to belong to more than
11.46 Where do the votes come from? In the election de scribed in Exercise 11.44, what percent of the candidate's votes come from black voters? (Write this as a conditional probabil ity and use the definition of conditional probability.)
11.45 Winning at tennis, continued. Based on your work in Exercise 11.43, in what percent of points won by the server was the first serve in? (Write this as a conditional probability and use the definition of conditional probability.)
11.44 Urban voters. The voters in a large city are 40%liix white, 40% black, and 20% Hispariic. (Hispanics may be of any race in official statistics, but here we are speaking of po litical blocks.) A black mayoral candidate anticipates attract ing 30% of the white vote, 90% of the black vote, and
11.43 Winning at tennis. A player serving in tennis has two chances to get a serve into play. If the first serve is out, the player serves again. If the second serve is also out, the player loses the point. Here are probabilities based on four years of the Wimbledon Championship:^®P(lst serve in)
11.42 The geometric distributions. You are tossing a pair of balanced dice in a board game. Tosses are indeperident. You land in a danger zone that requires you to roll doubles (both faces show the same laumber of spots) before you are allowed to play again. How long will you wait to play again?(a)
11.41 Julie's conditional probabilities. If Julie is offered the _ federal job, what is the conditional probability that she is also r offered the New Jersey job? If Julie is offered the New Jersey job, what is the conditional probability that she is also offered the federal job?
11.40 Will Julie get just these offers? What is the proba bility that Julie is offered both the Coianecticut and New Jersey jobs, but not the federal job?
11.39 Will Julie get a job offer? What is the probability that Julie is offered at least one of the three jobs?
11.38 Deer and pine seedlings. In the setting of Exercise 11.36, what percent of the trees that were not damaged by deer were more than 2/3 covered by thorny plants?
11.37 Deer and pine seedlings. In the setting of Exercise 11.36, what percent of the trees that were damaged by deer were less than 1/3 covered by thorny plants?
11.36 Deer and pine seedlings. As suburban gardeners know, deer will eat almost anything green. In a study of pine seedlings at an environmental center in Ohio, researchers noted how deer damage varied with how much of the seedling was covered by thorny undergrowth:'Deer Damage Thorny cover Yes No
11.35 College degrees. Exercise 11.34 gives the counts (in thousands) of earned degrees in the United States in the 2010-2011 academic year. Use these data to answer the following questions.(a) What is the probability that a randomly chosen degree re cipient is a man?(b) What is the conditional
11.34 College degrees. A striking trend in higher education is that more women than men reach each level of attainment.Here are the counts (in thousands) of earned degrees in the United States in the 2010-2011 academic year, classified by level and by the sex of the degree recipient:®(a) If you
11.33 A probability teaser. Suppose (as is roughly correct)that each child born is equally likely to be a boy or a girl and that the sexes of successive children are independent. If we let BO mean that the older child is a boy and the younger child is a girl, then each of the combinations BB, BO,
11.32 Computer games. Here is the distribution of com puter games sold by type of game:^Game type Strategy Role playing Family entertainment Shooters Children's Other Probability 0.354 0.139 0.127 0.109 0.057 0.214 What is the conditional probability that a computer game is a role-playing game,
11.31 Income tax returns. Here is the distribution of the adjusted gross income (in thousands of dollars) reported on in dividual federal income tax returns in 2006:Income < 15 15-49 50-99 100-199 > 200 Probability j 0.272 0.394 0.217 0.087 0.030(a) What is the probability that a randomly chosen
11.30 Foreign-language study. Choose a student in grades 9 to 12 at tandom and ask if he or she is studying a language othet than English. Here is the distribution of results:Language Spanish French German All others None Prohahility I 0.26 0.09 0.03 0.03 0.59 What is the conditional probability
11.29 Screening job applicants. A company retains a psychologist to assess whether job applicants ate suited for assembly-line work. The psychologist classifies applicants as one of A (well suited), B (marginal), or C (not suited). The company is concerned about the event D that an employee leaves
11.28 Tendon surgery. You have totn a tendon and ate■He facing surgery to repair it. The surgeon explains the risks to you: infection occurs in 3% of such operations, the tepair fails in 14%, and both infection and failure occur together in 1 %. What percent of these operations succeed and are
11.27 Getting into college. Ramon has applied to both Princeton and Stanford. He thinks the probability that Prince ton will admit him is 0.4, the probability that Stanford will admit him is 0.5, and the probability that both will admit him is 0.2. Make a Venn diagram. Then answer these
11.26 A random walk on Wall Street? The "random walk"theory of stock prices says that price movements irt disjoint time periods are independent of each othet. Suppose that we record only whether the price is up or down each year, and that the probability that our portfolio rises in price in any one
11.25 Playing the slots. Before electronics took ovet, slot machines wete like this: you pull the lever to spin three wheels;each wheel has 20 symbols, all equally likely to show when the wheel stops spinning; the three wheels are independent of each other. Suppose that the middle wheel has 9
11.24 Universal blood donors. People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population have O-negative blood. If 10 people appear at ran dom to give blood, what is the probability that at least 1
11.23 Playing the lottery. New York State's "Quick Draw"lottery moves right along. Players choose between one and ten numbers from the range 1 to 80; 20 winning numbers are dis played on a screen every four minutes. If you choose just one number, your prohahility of winning is 20/80, or 0.25.
11.22 Of people who died in the United States in recent years, 86% were white, 12% were black, and 2% were Asian.(This ignores a small number of deaths among other races.)Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. The prohahility that a ran domly chosen
11.21 Let Abe the event that a victim of violent death was a woman and B the event that the death was a suicide. The propottion of suicides among violent deaths of women is expressed in prohahility notation as(a) P(Aaiul B). (h)P(A|B). (c) P(B | A).
11.20 The conditional probability that the death was acciden tal, given that the victim was male, is about(a) 0.81. (b) 0.78. (c) 0.56.
11.19 The conditional probability that the victim was male, given that the death was accidental, is about(a) 0.81. (b) 0.78. (c) 0.56.
11.18 Choose a violent death in this age group at random. The probability that the victim was male is about(a) 0.81. (b) 0.78. (c) 0.19.
11.17 Choose an American adult at random. The probability that you choose a woman is 0.52. The probability that the per son you choose has never married is 0.25. The probability that you choose a woman who has never married is 0.11. The prob ability that the person you choose is either a woman or
11.16 An instant lottery game gives you probability 0.02 of winning on any one play. Plays are independent of each other.If you play 3 times, the probability that you win on none of your plays is about(a) 0.98. (b) 0.94. (c) 0.000008.
11.15 False HIV positives. Continue your work from Exercise 11.13. What is the probability that a person has the antibody, given that the test is positive? (Your result illustrates a fact that is important when coiasidering proposals for widespread testing for HIV, illegal drugs, or agents of
11.14 Peanut and tree nut allergies. Continue your work from Exercise 11.12. What is the conditional probability that exactly 1 of the people will be allergic to peanuts or tree nuts, given that at least 1 of the 5 people suffers from one of these allergies?
11.13 Testing for HIV. Enzyme immunoassay tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is not always correct. Here are approximate probabilities of positive
11.12 Peanut and tree nut allergies. About 1% of the American population is allergic to peanuts or tree nuts.' Choose 5 individuals at random and let the random variable Xbe the number in this sample who are allergic to peanuts or tree nuts. The possible values X can take are 0, 1, 2, 3, 4, and 5.
11.11 The probability of a flush. A poker player holds a flush when all 5 cards in the hand belong to the same suit (clubs, diamonds, hearts, or spades). We will find the probability of a flush when 5 cards are dealt. Remember that a deck contains 52 cards, 13 of each suit, and that when the deck
11.10 Teens online. We saw in Example 11.8 that 93% of teenagers are online and that 55%of online teens have posted a profile on a social networking site. Of online teens with a profile, 76% have placed comments on a friend's blog. What percent of all teens are online, have a profile, and comment
11.9 At the gym. Suppose that 10% of adults belong to health clubs, and 40% of these health club members go to the club at least twice a week. What percent of all adults go to a health club at least twice a week? Write the information given in terms of probabilities and use the general
11.8 Independent? The Clemson University Fact Book for 2007 shows that 123 of the uni versity's 338 assistant professors were women, along with 76 of the 263 associate profes sors and 73 of the 375 full professors.(a) What is the probability that a randomly chosen Clemson professor iis a woman;(b)
11.7 Distance learning. In the setting of Exercise 11.5, what is the conditional probability that a student is local, given that he or she is less than 25 years old?
11.6 College degrees. In the setting of Exercise 11.4, what is the conditional probability that a degree is earned by a woman, given that it is a bachelor's degree?
11.5 Distance learning. A study of the students taking distance learning courses at a univer sity finds that they are mostly older students not living in the university town. Choose a distance learning student at random. Let A be the event that the student is 25 years old or older and B the event
11.4 College degrees. Of all college degrees awarded in the United States, 50% are bach elor's degrees, 59% are earned by women, and 29% are bachelor's degrees earned by women. Make a Venn diagram and use it to answer these questions.(a) What percent of all degrees are earned by men?(b) What
11.3 Lost Internet sites. Internet sites often vaiaish or move, so that refereiaces to them can't be followed. In fact, 13% of Internet sites referenced in major scientific journals are lost within two years after publication.^ If a paper contains seven Internet references, what is the ptohability
11.2 Common names. The Census Bureau says that the 10 most common names in the United States are (in order) Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for 9.6% of all U.S. residents. Out of curiosity, you look at the authors of the
11.1 Older college students. Government data show that 8% of adults are full-time college students and that 30% of adults are age 55 or older. Nonetheless, we can't conclude that, because (0.08)(0.30) = 0.024, about 2.4% of adults are college students 55 or older. Why not?
10.32 Playing the numbers: the house has a business.Unlike Joe (see the previous exercise) the operators of the numbers racket can rely on the law of large numbers. It is said that the New York City mobster Casper biolstein took as many as 25,000 bets per day in the Prohibition era. That's 150,000
10.31 Playing the numbers: a gambler gets chance out comes. The law of large ntimbers tells us what happens in the long run. Like many games of chance, the numbers racket has outcomes so variable—one three-digit number wins $600 and all others win nothing—that gamblers never reach "the long
10.30 Playing the numbers. The numbers racket is a wellentrenched illegal gambling operation in most large cities. One version works as follows: you choose one of the 1000 three-digit numbers 000 to 999 and pay your local numbers runner a dollar to enter your bet. Each day, one three-digit number
10.29 Sampling male students, continued. To estimate the mean height /u of male students on your campus, you will measure an SRS of students. You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. You want your sample mean x to
10.28 Sampling male students. To estimate the mean height jtt of male students on your campus, you will measure an SRS of students. Yt)u know from government data that heights of young men are approximately Normal with standard devi ation about 2.8 inches. How large an SRS must you take to reduce
10.27 Airline passenger weights. The Federal Aviallli« tion Administration tells airlines to assume that passengets average 190 pounds in the summer, including clothing and carry-on baggage. But passengers vary, and the FAA does not specify a standard deviation. A reasonable standard de viation is
10.26 Returns on stocks. Andrew plans to retire in Hi' 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century the real (that is, ad justed for inflation) annual returns on U.S. common stocks had
10.25 Auto accidents. Tbe number of accidents per week at a hazardous intersection varies with mean 2.2 and standard de viation 1.4. This distribution takes only whole-number values, so it is certainly not Normal.(a) Let X be the mean number of accidents per week at the in tersection duting a year
10.24 Pollutants in auto exhausts. The entire fleet of light vehicles sold in the United States by any manufacturer must emit an average of no more than 0.07 grams per mile (g/mi)of nitrogen oxides (NOX). NOX emissions for one car model vary Normally with mean 0.05 g/mi and standard deviation 0.01
10.23 Durable press fabrics. "Durable press" cotton fabrics are treated to improve their recovery from wrinkles after wash ing. Unfortunately, the treatment also reduces the strength of the fabric. The breaking strength of untreated fabric is Nor mally distributed with mean 58 pounds and standard
10.22 Glucose testing. A pregnant women is classified as having gestational diabetes if her blood glucose level is above 140 milligrams per deciliter (mg/dl) one hour after having a sugary drink. The glucose level isn't fixed, but varies from day to day. Shelia's glucose level one hour after the
10.21 Heights of male students. To estimate the mean height IX of male students on your campus, you will measure an SRS of students. Heights of people of the same sex and similar ages are close to Normal. You know from government data that the standard deviation of the heights of young men is about
10.20 Lightning strikes. The number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. (These values are typical of much of the United States.) The National Lightning Detection Net work uses automatic sensors to watch for lightning in a sample
10.19 Roulette. A 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.One of the simplest wagers chooses red or hlack. A bet of $1 on red returns $2 if the ball lands in a red slot.
10.18 Small classes In school. The Tennessee STAR ex periment randomly assigned children to regular or small classes during their first four years of school. When these children reached high school, 40.2% of blacks from small classes took the ACT or SAT college entrance exams. Only 31.7% of blacks
10.17 Testing glass. How well materials conduct heat mat ters when designing houses. As a test of a new measurement process, 10 measurements are made on pieces of glass known to have conductivity 1. The average of the 10 measurements is 1.09. Is each of the boldface numbers a parameter or a
10.16 The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days.The probability that the average pregnancy length for 6 ran domly chosen women exceeds 270 days is about(a) 0.40. (b)
10.15 The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that (a) as we look at more and more bulbs, their average burnout time gets ever closer to the mean for all bulbs
10.14 Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT math scores. If you do this many times, the standard deviation of the average scores you get will be close to
10.13 Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT math scores. If you do this many times, the mean of the average scores you get will be close to (a) 515. (b)
10.12 Annual returns on the more than 5000 common stocks available to investors vary a lot. In a recent year, the mean re- turn was 8.3% and the standard deviation of returns was 28.5%. The law of large numbers says that10.15 The number of hours a light bulb burns before failing varies from bulb to
10.11 A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. The boldface number is a (a) sampling distribution. (b) parameter. (c)
10.10 The Bureau of Labor Statistics announces that last month it interviewed all members of the labor force in a sam- ple of 60,000 households; 4.9% of the people interviewed were unemployed. The boldface number is a (a) sampling distribution. (b) parameter. (c) statistic.
10.9 More on insurance. An insurance company knows that in the entire population of millions of homeowners, the mean annual loss from fire is fi = $250 and the standard deviation of the loss is cr = $1000. The distribution of losses is strongly right-skewed;most policies have $0 loss, but a few
10.8 Larger sample, more accurate estimate. The blood cholesterol level of all men aged 20 to 34 follows a population distribution with mean fx = 188 milligrams per deciliter(mg/dl) and standard deviation cr = 41 mg/dl.(a) Choose an SRS of 100 men ftom this population. According to the central
10.7 Population versus sample. The blood cholestetol level of all men aged 20 to 34 fol lows the Normal distribution with mean fx = 188 milligrams per deciliter (mg/dl) and standard deviation ct= 41 mg/dl. A sample survey measures the blood cholesterol level of an SRS of 10 such men.(a) What are

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