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statistics alive
Questions and Answers of
Statistics Alive
6.36 Compatible donors Refer to the previous exercise. Let the random variable X = number of compatible donors.Check the conditions for X to be binomial by answering parts a–c.a. What constitutes a
6.35 Kidney transplants In kidney transplantations, compatibility between donor and receiver depends on such factors as blood type and antigens. Suppose that for a randomly selected donor from a
6.51 Binomial assumptions For the following random variables, check whether the conditions needed to use the binomial distribution are satisfied or not. Explaina. X = number of people suffering from
6.52 Grandparents Let X = the number of living grandparents that a randomly selected adult American has. According to recent General Social Surveys, its probability distribution is approximately P102
6.69 Global warming Suppose that weekly use of gasoline for motor vehicle travel by adults in North America has approximately a normal distribution with a mean of 20 gallons and a standard deviation
6.68 Used car deals Refer to the previous exercise. Suppose carmax.com decides to highlight any used car that is priced 1.5 standard deviations below the mean price as a special deal on its Web
6.67 Used car prices Data from the Web site carmax.com compiled in July 2014 show that prices for used Audi A4 cars advertised on the Web site have a mean of $23,800 and a standard deviation of
6.66 Gestation times For 5459 pregnant women using Aarhus University Hospital in Denmark in a two-year period who reported information on length of gestation until birth, the mean was 281.9 days,
6.65 Cloning butterflies The wingspans of recently cloned monarch butterflies follow a normal distribution with mean 9 cm and standard deviation 0.75 cm. What proportion of the butterflies has a
6.64 Female heights Female heights in North America follow a normal distribution with m = 65 inches and s = 3.5 inches. Find the proportion of females who area. under five feet.b. over six feet.c.
6.62 Boys and girls birth weight Exercise 6.28 mentioned that in the United States, birth weight of boys is approximately normal, with mean 3.41 kg and standard deviation 0.55 kg. For girls, the
6.61 Quartiles If z is the positive number such that the interval within z standard deviations of the mean contains 50% of a normal distribution, thena. Explain why this value of z is about 0.67.b.
6.60 z-score and tail probabilitya. Find the z-score for the number that is less than only 1% of the values of a normal distribution. Sketch a graph to show where this value is.b. Find the z-scores
6.59 z-scores Find the z-score such that the interval within z standard deviations of the mean contains probability(a) 0.95 and (b) 0.99 for a normal distribution. Sketch the two cases on a single
6.58 Normal probabilities For a normal distribution, find the probability that an observation isa. Within 1.96 standard deviations of the mean.b. More than 2.33 standard deviations from the mean.
6.57 Flyers’ insurance An insurance company sells a policy to airline passengers for $1. If a flyer dies on a given flight (from a plane crash), the policy gives $100,000 to the chosen beneficiary.
6.56 Are you risk averse? You need to choose between two alternative programs for dealing with the outbreak of a deadly disease. In program 1, 200 people are saved. In program 2, there is a 2>3
6.55 Paths to school You have two possible paths to reach your school. Path A is 1.5 km long and path B is 1.3 km long. Each day, the probability you choose path A to reach school is 3/4 and this
6.54 Auctioning paintings A collector is interested in two paintings by the same artist available at an auction. She plans to bid $3,000 for the first painting auctioned off and$2,000 for the second.
6.34 Relative grades The mean and standard deviation of the grades of a statistics course and an English course are 1m = 80, s = 4.52 and 1m = 85, s = 4.02, respectively.A student attends both the
5.81 Conference dinner Of the participants at a conference, 50% attended breakfast, 90% attended dinner, and 40%attended both breakfast and dinner. Given that a participant attended breakfast, find
5.61 DNA evidence compelling? DNA evidence can be extracted from biological traces such as blood, hair, and saliva. “DNA fingerprinting” is increasingly used in the courtroom as well as in
5.59 Was OJ actually guilty? Former pro football star O. J. Simpson was accused of murdering his wife. In the trial, a defense attorney pointed out that although Simpson had been guilty of earlier
5.58 More screening for breast cancer Refer to the previous exercise. For young women, the prevalence of breast cancer is lower. Suppose the sensitivity is 0.86 and the specificity is 0.88, but the
5.57 Mammogram diagnostics Breast cancer is the most common form of cancer in women, affecting about 10%of women at some time in their lives. There is about a 1%chance of having breast cancer at a
5.56 Rosencrantz and Guildenstern In the opening scene of Tom Stoppard’s play Rosencrantz and Guildenstern Are Dead, about two Elizabethan contemporaries of Hamlet, Guildenstern flips a coin 91
5.55 A true coincidence of emergency E-Comm, British Columbia’s emergency communications center, provides communication services and support systems to two million residents of southwest British
5.54 Monkeys typing Shakespeare Since events of low probability eventually happen if you observe enough trials, a monkey randomly pecking on a typewriter could eventually write a Shakespeare play
5.53 Coincidence in your life State an event that has happened to you or to someone you know that seems highly coincidental (such as seeing a friend while on vacation).Explain why that event may not
5.52 Horrible 11 on 9/11 The digits in 9/11 add up to 11 19 + 1 + 12, American Airlines flight 11 was the first to hit the World Trade Towers (which took the form of the number 11), there were 92
5.51 Failure and repair of photocopiers In a photocopy center, there are two small photocopiers, two medium photocopiers and one big photocopier. The probability that a small one fails and requires
5.50 Holes in one at Masters The Augusta National Golf Course in Augusta, Georgia, hosts the Masters Tournament each April. The course consists of four par 3s, ten par 4s, and four par 5s. The par 4s
5.49 Lots of pairs Show that with 25 students, there are 300 pairs of students who can have the same birthday. So it’s really not so surprising if at least two students have the same birthday.
5.48 Matching your birthday You consider your birth date to be special since it falls on January 1. Suppose your class has 25 students.a. Is the probability of finding at least one student with a
5.47 Heart disease A particular heart disease is said to have a prevalence of 1/1000 in a specific population. In a sample of 50 people chosen randomly, what is the probability that at least two
5.46 Checking independence In each of three independent visits to a restaurant, you choose randomly between two of today’s specials, TS1 and TS2, on the menu. Let A denote{today’s special on
5.62 Triple Blood Test Example 8 about the Triple Blood Test for Down syndrome found the results shown in the table on next column.a. Estimate the probability that Down syndrome occurs 1Down =
5.63 Simulating arrivals to local holiday center The director of a local holiday center is offering a special prize to the first married visitor. The distribution of the marital status for Americans
5.64 Probability of winning In Example 16, we estimated the probability of winning the game was 0.65.a. If you conducted 30 more simulations of this game, what probability of winning would you expect
5.80 Passing scores Suppose you need a score of 70 out of 100 to pass an exam. Let B denote the event you score at least 85 and D denote the event you pass the exam.Assume P1B2 = 0.3 and P1D2 =
5.79 Car and phone You want to buy a car and a phone from a selection of 4 models and 6 models, respectively. Supposing all the models are equally likely to be chosen, denote the outcomes of your
5.78 Laundry detergent A manufacturer of laundry detergent has introduced a new product that it claims to be more environmentally sound. An extensive survey gives the percentages shown in the
5.77 Teens and parents In the CASA teen survey described in the previous exercise, 33% of teens reported that parents are never present at parties they attend. Thirtyone percent of teens who say
5.76 Teens and drugs In August 2006 the Center on Addiction and Substance Abuse (CASA) at Columbia University reported results of a survey of 1297 teenagers about their views on the use of illegal
5.75 Health insurance According to a 2006 census bureau report, 59% of Americans have private health insurance, 25%have government health insurance (Medicare or Medicaid or military health care), and
5.74 Independent on coffee? Students in a geography class are asked whether they’ve visited Europe in the past 12 months and whether they’ve flown on a plane in the past 12 months.a. For a
5.73 Driver’s exam Three 15-year-old friends with no particular background in driver’s education decide to take the written part of the Georgia Driver’s Exam. Each exam was graded as a pass (P)
5.72 Death penalty jury In arguing against the death penalty, Amnesty International has pointed out supposed inequities, such as the many times a black person has been given the death penalty by an
5.71 Life after death In a General Social Survey, in response to the question “Do you believe in life after death?” 1455 answered yes and 332 answered no.a. Based on this survey, estimate the
5.70 Caught doctoring the books After the major accounting scandals with Enron, a large energy company, the question may be posed, “Was there any way to examine Enron’s accounting books to
5.69 Choices for lunch For the set lunch at Amelia’s Restaurant, customers can select one meat dish, one vegetable, one beverage, and one dessert. The menu offers two meats (beef and chicken),
5.68 P(life after death) Explain the difference between the relative frequency and subjective definitions of probability.Illustrate by explaining how it is possible to give a value for (a) the
5.67 Due for a boy? A couple has five children, all girls. They are expecting a sixth child. The father tells a friend that by the law of large numbers the chance of a boy is now much greater than
5.66 Peyton Manning completions As of the end of the 2010 NFL season, Indianapolis Colts quarterback Peyton Manning, throughout his 13-year career, completed 65%of all of his pass attempts. Suppose
5.65 Probability of winning In Example 16, we explored the number of rolls it takes to win the game. In reality, it’s not the number of rolls but rather the time it takes to move 12 spaces that
5.45 Online sections For a course with two sections, let A denote {first section is online}, let B denote (at least one section is online}, and let C denote {both sections are online}.Suppose P (a
5.44 Big loser in Lotto Example 10 showed that the probability of having the winning ticket in Lotto South was 0.00000007.Find the probability of holding a ticket that has zero winning numbers out of
5.43 Drawing more cards A standard deck of poker playing cards contains four suits (clubs, diamonds, hearts, and spades) and 13 different cards of each suit. During a hand of poker, 5 of the 52 cards
5.23 Seat belt use and auto accidents Based on records of automobile accidents in a recent year, the Department of Highway Safety and Motor Vehicles in Florida reported the counts who survived (S)
5.22 Pick the incorrect statement Which of the following statements is not correct, and why?a. Last night, you randomly selected a restaurant for dinner from three similar restaurants in your city,
5.21 Insurance Every year the insurance industry spends considerable resources assessing risk probabilities. To accumulate a risk of about one in a million of death, you can drive 100 miles, take a
5.20 Pick the incorrect statement Which of the following statements is not correct, and why?a. If the number of male and female employees at a call center is equal, then the probability you call four
5.19 Three children A couple plans to have three children.Suppose that the probability of any given child being female is 0.5, and suppose that the genders of each child are independent events.a.
5.18 On-time arrival probabilities The all-time, on-time arrival rate of a certain airline to a specific destination is 82%. This week, you have booked two flights to this destination with this
5.17 Curling In the sport of curling, each shot is given points on a scale from 0–5, rating the success of each. Your friend claims, “Since the sum of points awarded when two shots are made is
5.16 More true-false questions Your teacher gives a true-false pop quiz with 10 questions.a. Show that the number of possible outcomes for the sample space of possible sequences of 10 answers is
5.15 Pop quiz A teacher gives a four-question unannounced true-false pop quiz, with two possible answers to each question.a. Use a tree diagram to show the possible response patterns in terms of
5.14 Songs Out of 100 songs on a playlist, 15 are of your favorite artist. You decide to randomly play one track from this playlist.a. State the sample space for the possible outcomes.b. State the
Student union poll Part of a student opinion poll at a university asks students what they think of the quality of the existing student union building on the campus.The possible responses were great,
Stock market randomness An interview in an investment magazine (In the Vanguard, Autumn 2003) asked mathematician John Allen Paulos, “What common errors do investors make?” He answered, “People
5.11 Unannounced pop quiz A teacher announces a pop quiz for which the student is completely unprepared. The quiz consists of 100 true-false questions. The student has no choice but to guess the
5.10 Simulate coin flips Use the web app Random Numbers(go to the tab that says Coin Flips) on the book’s website or other software (such as random.org/coin) to illustrate the long-run definition
5.9 Nuclear war You are asked to use your best judgment to estimate the probability that there will be a nuclear war within the next 10 years. Is this an example of relative frequency or subjective
5.8 Heart transplant Before the first human heart transplant, Dr. Christiaan Barnard of South Africa was asked to assess the probability that the operation would be successful. Did he need to rely on
Protecting the environment When the General Social Survey most recently asked subjects whether they are a member of an environmental group (variable GRNGROUP) and whether they would be willing to pay
Global warming and trees A survey asks subjects whether they believe that global warming is happening (yes or no)and how much fuel they plan to use annually for automobile driving in the future,
Newspaper sales You are the director of newspaper sales for the local paper. Each customer has signed up for either weekday delivery or weekend delivery. You record whether he or she received the
5.42 Discussion with students In a statistics class of 30 students, 20 students are from the business program and 10 students are from the science program. The instructor randomly select three
5.41 Answering homework questions Each question of an online homework consists of two parts. The probability that you answer the first part of a given question correctly is 0.75. Given that you
5.40 Petra Kvitova serves Petra Kvitova of the Czech Republic won the 2014 Wimbledon Ladies’ Singles Championship. In the final game against Eugenie Bouchard of Canada she had 41 first serves, of
5.39 Happiness in relationship Are people happy in their romantic relationships? The table shows results from the 2012 General Social Survey for adults classified by gender and happiness.a. Estimate
5.38 Obesity in America A 2014 Gallup poll reported that 27%of people in the United States are obese (having a body mass index score of 30 or more). Blacks have the highest obesity rate at 35%,
5.37 Down syndrome again Example 8 discussed the Triple Blood Test for Down syndrome, using data summarized in a table shown again below.a. Given that a test result is negative, show that the
5.36 Homeland security According to an article in The New Yorker (March 12, 2007), the Department of Homeland Security in the United States is experimenting with installing devices for detecting
5.35 Identifying spam An article4 on www.networkworld.com about evaluating e-mail filters that are designed to detect spam described a test of MailFrontier’s Anti-Spam Gateway(ASG). In the test,
5.34 Go Celtics! Larry Bird, who played pro basketball for the Boston Celtics, was known for being a good shooter.In games during 1980–1982, when he missed his first free throw, 48 out of 53 times
5.33 Revisiting seat belts and auto accidents The following table is from Exercise 5.23 classifying auto accidents by survival status 1S = survived, D = died2 and seat belt status of the individual
5.32 Labor force In 2014, a sample of 1925 Americans revealed that about 20.5% of them belong to the government sector. 7.5% of these are part-time employees, 60%are full-time employees, and 32.5%
5.31 Religious affiliation The 2012 Statistical Abstract of the United States3 provides information on individuals’self-described religious affiliations. The information for 2008 is summarized in
5.30 Audit and low income Table 5.3 on audit status and income follows. Show how to find the probability of:a. Being audited, given that the taxpayer is in the lowest income category.b. Being in the
5.29 Smoke alarms statistics National estimates of reported fires derived from the National Fire Incident Reporting System (NFIRS) and the National Fire Protection Association’s (NFPA’s) fire
Recidivism rates A 2014 article from Business Insider(http://www.businessinsider.com/department-of-justicereport-shows-high-recidivism-rate-2014-4) discusses recidivism rates in the United States.
Arts and crafts sales A local downtown arts and crafts shop found from past observation that 20% of the people who enter the shop actually buy something. Three potential customers enter the shop.a.
5.7 Sample size and sampling accuracy Your friend is interested in estimating the proportion of people who would vote for his project in a local contest. He selects a large sample among his many
6.33 SAT versus ACT SAT math scores follow a normal distribution with an approximate m = 500 and s = 100.Also ACT math scores follow a normal distrubution with an approximate m = 21 and s = 4.7. You
5.76 Teens and drugs In August 2006 the Center on Addiction and Substance Abuse (CASA) at Columbia University reported results of a survey of 1297 teenagers about their views on the use of illegal
5.55 A true coincidence of emergency E-Comm, British Columbia’s emergency communications center, provides communication services and support systems to two million residents of southwest British
5.54 Monkeys typing Shakespeare Since events of low probability eventually happen if you observe enough trials, a monkey randomly pecking on a typewriter could eventually write a Shakespeare play
5.53 Coincidence in your life State an event that has happened to you or to someone you know that seems highly coincidental (such as seeing a friend while on vacation).Explain why that event may not
5.52 Horrible 11 on 9/11 The digits in 9/11 add up to 11 19 + 1 + 12, American Airlines flight 11 was the first to hit the World Trade Towers (which took the form of the number 11), there were 92
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