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intro stats
Stats Data And Models 5th Global Edition Richard De Veaux, Paul Velleman, David Bock - Solutions
Battery The life span of a calculator battery is Normally distributed with a mean of 45 hours and a standard deviation of 5 hours. What is the probability that a battery lasts more than 53 hours?
Assuming that the second 9 has the same mean and standard deviation, what is the mean and standard deviation of his total score if he plays a full 18 holes?SECTION 14.4
Golf scores A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of
Salary An employer pays a mean salary for a 5-day workweek of $1250 with a standard deviation of $129. On the weekends, his salary expenses have a mean of $450 with a standard deviation of $57. What is the mean and standard deviation of his total weekly salaries?
A certain company believes that 95% of its job applicants are trustworthy. The company gives everyone a polygraph test, asking, “Have you ever stolen anything from your place of work?”Naturally, all the applicants answer “No,” but the polygraph identifies some of those answers as lies,
Polygraphs Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of their hiring process in the hope that they can avoid hiring people who might be dishonest. There has been some research, but no
HIV testing In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of tests conducted were (correctly) positive, while for people without HIV 98.5% of the tests were (correctly)
Parts A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. The company prefers to use supplier A because only 1% of those connectors prove to be defective, but supplier A can deliver only 70% of the connectors needed. The
Dishwashers Dan’s Diner employs three dishwashers. Al washes 40% of the dishes and breaks only 1% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 1% of hers, but Chuck breaks 3% of the dishes he washes. (He, of course, will need a new job soon. . . .)You go
No-shows An airline offers discounted “advance-purchase” fares to customers who buy tickets more than 30 days before travel and charges “regular” fares for tickets purchased during those last 30 days. The company has noticed that 60% of its customers take advantage of the advance-purchase
Drunks Police often set up sobriety checkpoints—roadblocks where drivers are asked a few brief questions to allow the officer to judge whether or not the person may have been drinking. If the officer does not suspect a problem, drivers are released to go on their way. Otherwise, drivers are
E-readers II Given the e-reader data presented in Exercise 52:a) If a randomly selected U.S. adult has an e-reader, what is the probability that he or she hasn’t read an e-book in the past year?b) Is it more or less likely that a randomly selected U.S. adult who does not own an e-reader would
Absenteeism, part II At the company described in Exercise 51, what percent of the absent employees are on the night shift?
E-readers PewInternet reported in January of 2014 that 32% of U.S. adults own at least one e-reader, and that 28% of U.S.adults read at least one e-book in the previous year (and thus, presumably, owned an e-reader). Overall, 76% of U.S. adults read at least one book (electronic or otherwise) in
Absenteeism A company’s records indicate that on any given day about 1% of their day-shift employees and 2% of the nightshift employees will miss work. Sixty percent of the employees work the day shift.a) Is absenteeism independent of shift worked? Explain.b) What percent of employees are absent
Graduation, part II What percent of students who graduate from the college in Exercise 48 attended a public high school?
Suppose that the market researcher asks the household whether they enjoy the station’s sports programs first and gets yes for an answer. What is the probability that the household also enjoys the music programs?
Television again Recall Exercise
Graduation A private college report contains these statistics:70% of incoming freshmen attended public schools.75% of public school students who enroll as freshmen eventually graduate.90% of other freshmen eventually graduate.a) Is there any evidence that a freshman’s chances to graduate may
Television A television station conducting market research on its viewership finds that 21% of households enjoy its music programs. If a household enjoys its music programs, the chance that it also enjoys its sports programs is 71%, but if not, the chance that it also enjoys its sports programs is
Cars A random survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. Is country of origin independent of type of driver? Origin Driver Student Staff American 107 105 European 33 12 Asian 55 47
Gender A poll conducted by Gallup classified respondents by sex and political party, as shown in the table. Is party affiliation independent of the respondents’ sex? Explain. Democrat Republican Independent Male 32 28 34 Female 41 25 26
Snoring After surveying 995 adults, 81.5% of whom were over 30, the National Sleep Foundation reported that 36.8% of all the adults snored. 32% of the respondents were snorers over the age of 30.a) What percent of the respondents were 30 or less and did not snore?b) Is snoring independent of age?
Phone service According to estimates from the federal government’s 2010 National Health Interview Survey, based on face-to-face interviews in 16,676 households, approximately 63.6% of U.S. adults have both a landline in their residence and a cell phone, 25.4% have only cell phone service but no
Given the table of probabilities from Exercise 24, are gender and party affiliation independent? Explain. Gender Political Affiliation Conservative Labour Democrat Parties Liberal Other Will Not Vote Total Male 0.18 0.1 0.05 0.1 0.06 0.49 Female 0.19 0.12 0.05 0.08 0.07 0.51 Total 0.37 0.22 0.1
Men’s health again Given the table of probabilities from Exercise 23, are high blood pressure and high cholesterol independent? Explain. Cholesterd Blood Pressure High OK High 0.11 0.21 OK 0.16 0.52
Birth order, finis In Exercises 20 and 26, we looked at the birth orders and college choices of some Intro Stats students. For these students:a) Are enrolling in Agriculture and Human Ecology disjoint?Explain.b) Are enrolling in Agriculture and Human Ecology independent? Explain.c) Are being
Unsafe food Early in 2010, Consumer Reports published the results of an extensive investigation of broiler chickens purchased from food stores in 23 states. Tests for bacteria in the meat showed that 62% of the chickens were contaminated with campylobacter, 14% with salmonella, and 9% with both.a)
Pets, again The local animal shelter in Exercise 22 reported that it currently has 24 dogs and 18 cats available for adoption;8 of the dogs and 6 of the cats are male. Are the species and sex of the animals independent? Explain.
Cards If you draw a card at random from a well-shuffled deck, is getting an ace independent of the suit? Explain.
School again According to Exercise 16, in a particular school, 45% of pupils have another sibling in the same school, 28% of pupils have another relative who is not a sibling, and 15% of pupils have both siblings and other relatives.a) What is the probability that a pupil who has a sibling in the
Public health A public health department knows that the chance that a country resident contracts some form of cancer in his life is 30%, the chance that a resident has private health insurance is 25%, and the chance that a resident being treated for cancer has private health insurance is 7.5%. For
In a particular city, 53% of workers use their car to go to work, 45% use public transport, and 18% use both means of transport.We select a worker at random.a) What is the probability that the worker uses neither a car nor public transport to go to work?b) What is the probability that the worker
Eligibility A university requires its biology majors to take a course called BioResearch. The prerequisite for this course is that students must have taken either a statistics course or a computer course. By the time they are juniors, 52% of the biology majors have taken statistics, 23% have had a
Shirts The soccer team’s shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extra-large shirts. You want a medium for you and one for your sister. Find the probability of each event described.a) The first
Batteries A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome.a) The first two you choose are both good.b) At least one of the first three works.c) The first four you
Another hand You pick three cards at random from a deck.Find the probability of each event described below.a) You get no aces.b) You get all hearts.c) The third card is your first red card.d) You have at least one diamond.
Cards You are dealt a hand of three cards, one at a time. Find the probability of each of the following.a) The first heart you get is the third card dealt.b) Your cards are all red (that is, all diamonds or hearts).c) You get no spades.d) You have at least one ace.
Sick cars Twenty percent of cars that are inspected have faulty pollution control systems. The cost of repairing a pollution control system exceeds $100 about 40% of the time. When a driver takes her car in for inspection, what’s the probability that she will end up paying more than $100 to
Sick kids Seventy percent of kids who visit a doctor have a fever, and 30% of kids with a fever also have sore throats.What’s the probability that a kid who goes to the doctor has a fever and a sore throat?
Birth order, take 2 Look again at the data about birth order of Intro Stats students and their choices of colleges shown in Exercise 20.a) If we select a student at random, what’s the probability the person is an Arts and Sciences student who is a second child(or more)?b) Among the Arts and
Global survey, take 2 Look again at the table summarizing the Roper survey in Exercise 19.a) If we select a respondent at random, what’s the probability we choose a person from the United States who has done post-graduate study?b) Among the respondents who have done post-graduate study, what’s
Polls The table shows the political affiliations of British voters with clear voting intentions according to gender in a YouGov poll in April 2017.a) What is the probability that i) a randomly chosen voter will vote Conservative?ii) a female voter votes Labour?iii) a voter who will vote for a party
Job application The probabilities that an applicant of a particular job has the required qualifications and/or the required experience are shown in the table.What’s the probability thata) an applicant has both required qualifications and experience?b) an applicant has required qualifications?c)
Pets In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male. Find each of the following conditional probabilities if an animal is selected at random:a) The pet is male, given that it is a
Cards You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities:a) The card is a heart, given that it is red.b) The card is red, given that it is a heart.c) The card is an ace, given that it is red.d) The card is a queen, given that it is a
Birth order A survey of students in a large Introductory Statistics class asked about their birth order 11 = oldest or only child2 and which college of the university they were enrolled in. Here are the data:Suppose we select a student at random from this class. What is the probability that the
Global survey The marketing research organization GfK Roper conducts a yearly survey on consumer attitudes worldwide.They collect demographic information on the roughly 1500 respondents from each country that they survey. Here is a table showing the number of people with various levels of education
Workers Employment data at a large company reveal that 72%of the workers are married, that 44% are college graduates, and that half of the college grads are married. What’s the probability that a randomly chosen workera) is neither married nor a college graduate?b) is married but not a college
Amenities A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TVs, and 21%had both a TV and a refrigerator. What’s the probability that a randomly selected dorm room hasa) a TV but no refrigerator?b) a TV or a refrigerator, but not both?c) neither a TV nor
School In a particular school, 45% of pupils have another sibling in the same school, and 28% of pupils have another relative who is not a sibling. Furthermore, 15% of pupils have both siblings and other relatives. What is the probability that a pupil chosen at random hasa) a sibling in the school
Smartphone Recent research suggests that 50% of people in the 30–49 age bracket chose “smartphone only” as their preferred means to access the Internet, 20% chose “desktop/laptop/tablet only,” while 27% chose “both.” What is the probability that a person in the 30–49 age bracket:a)
Online banking last time Given the probabilities in Exercise 12, what is the probability that a person is younger than 50 given that she uses online banking? Has the probability that she is younger than 50 increased or decreased with the additional information?CHAPTER EXERCISES
Internet final Given the probabilities in Exercise 11, what is the probability that a person is from the Asian continent and that they use the Internet? Has the probability that they are from the Asian continent increased or decreased with additional information?
Online banking again Suppose that the information in Exercise 10 had been presented in the following way. A national survey of bank customers finds that 40% are younger than 50.Of those younger than 50, 5 of 8 conduct their banking online.Of those older than 50, only 1 of 12 banks online. Draw a
Internet again Suppose that the information in Exercise 9 has been presented in the following way. 55% of the world population lives on the Asian continent. 51% of the Asian continent’s population use the Internet. On the other hand, 64% of the rest of the world’s population uses the Internet.
Online banking A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are younger than 50, and that 25% are younger than 50 and conduct their banking online. Make a probability table. Why is a table better than a tree here?
Internet usage The Asian continent contains 55% of the world population and 57% of the world’s population uses the Internet.Suppose that 29% of the world’s population does not live on the Asian continent and uses the Internet. Make a probability table.Why is a table better than a tree
Births If the sex of a child is independent of all other births, is the probability of a woman giving birth to a girl after having four boys greater than it was on her first birth? Explain.SECTION 13.4
Titanic On the Titanic, the probability of survival was 0.323.Among first-class passengers, it was 0.625. Were survival and ticket class independent? Explain.
Field goals A nervous kicker usually makes 70% of his first field goal attempts. If he makes his first attempt, his success rate rises to 90%. What is the probability that he makes his first two kicks?SECTION 13.3
Late to the train A student figures that he has a 30% chance of being let out of class late. If he leaves class late, there is a 45%chance that he will miss his train. What is the probability that it will cause him to miss the train?
Sports again From Exercise 3, if someone doesn’t like to watch basketball, what is the probability that she will be a football fan?
Sports What is the probability that a person likes to watch football, given that she also likes to watch basketball?Football No Football Basketball 27 13 No Basketball 38 22
Internship For a course program, the chance of being offered an internship at company A is 35%, the chance of being offered an internship at company B is 30%, while the chance of being offered an internship at both is 20%. What is the probability that a randomly selected applicant gets selected by
Pet ownership Suppose that 25% of people have a dog, 29% of people have a cat, and 12% of people own both. What is the probability that someone owns a dog or a cat?
Red cards You shuffle a deck of cards and then start turning them over one at a time. The first one is red. So is the second.And the third. In fact, you are surprised to get 10 red cards in a row. You start thinking, “The next one is due to be black!”a) Are you correct in thinking that
An interesting coincidence or a cosmic sign?a) What is the probability that the winning three numbers match the date on any given day?b) What is the probability that a whole year passes without this happening?c) What is the probability that the date and winning lottery number match at least once
9/11? On September 11, 2002, the first anniversary of the terrorist attack on the World Trade Center, the New York State Lottery’s daily number came up 9– 1–
Pepsi For a sales promotion, the manufacturer places winning symbols under the caps of 10% of all Pepsi bottles. You buy a six-pack. What is the probability that you win something?
Lights You purchased a five-pack of new light bulbs that were recalled because 6% of the lights did not work. What is the probability that at least one of your lights is defective?
Religion Census reports for a city indicate that 62% of residents classify themselves as Christian, 12% as Jewish, and 16%as members of other religions (Muslims, Buddhists, etc.). The remaining residents classify themselves as nonreligious. A polling organization seeking information about public
Union membership Suppose that in a particular city, 25% of workers have obligatory union membership and 30% of workers have voluntary union membership, while 45% of members do not belong to a workers’ union. You are conducting a poll by selecting workers from a database at random. In your first
The train To get to work, a commuter must cross train tracks.The time the train arrives varies slightly from day to day, but the commuter estimates he’ll get stopped on about 15% of work days. During a certain 5-day work week, what is the probability that hea) gets stopped on Monday and again on
Striker A certain football/soccer striker scores 14.6% of his shots.If his shots are independent, what is the probability that hea) makes three consecutive shots without a goal?b) scores his first goal on the second shot?c) scores at least once in the first two shots?d) scores all his first four
Slot machine A slot machine has three wheels that spin independently.Each has 10 equally likely symbols: 4 bars, 3 lemons, 2 cherries, and a bell. If you play, what is the probability thata) you get 3 lemons?b) you get no fruit symbols?c) you get 3 bells (the jackpot)?d) you get no bells?e) you get
Dice You roll a fair die three times. What is the probability thata) you roll all 6’s?b) you roll all odd numbers?c) none of your rolls gets a number divisible by 3?d) you roll at least one 5?e) the numbers you roll are not all 5’s?
Blood In Exercise 40, you calculated probabilities involving various blood types. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the events were
Disjoint or independent? In Exercise 39, you calculated probabilities of getting various M&M’s. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time.Other answers depended on the assumption that the events
Blood The American Red Cross says that about 51% of African-Americans have Type O blood, 26% Type A, 19%Type B, and the rest Type AB.a) An African-American volunteers to give blood. What is the probability that this donor i. has Type AB blood?ii. has Type A or Type B blood?iii. is not Type O?b)
at least one is green?
none are yellow?
the third one is the first one that’s red?
they are all brown?
it is striped?b) If you pick three M&M’s in a row, what is the probability ability that
it is not green?
it is yellow or orange?
it is brown?
M&M’s The Mars company says that before the introduction of purple, yellow candies made up 20% of their plain M&M’s, red another 20%, and orange, blue, and green each made up 10%.The rest were brown.a) If you pick an M&M at random, what is the probability that
Polling, part II According to Pew Research, the contact rate(probability of contacting a selected household) was 90% in 1997 and 62% in 2012. However, the cooperation rate (probability of someone at the contacted household agreeing to be interviewed)was 43% in 1997 and dropped to 14% in 2012.a)
Polling As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 62% of U.S.households, the percentage of those contacted who agree to cooperate with the survey fell from 43% in 1997 to 14% in
If we select two people at random from this sample,a) what is the probability that they think GM foods are worse?b) what is the probability that neither thinks that GM foods are worse?c) what is the probability that the first thinks GM foods are worse, and the second thinks GM foods are better?d)
GM foods revisited, revisited Consider again the results of the poll about GM foods discussed in Exercise
More Shootings Exercise 33 shows the results of a poll about shootings. Suppose we select four people at random from this sample.a) What is the probability that all four responded that they are very or somewhat worried?b) What is the probability that none responded that they are very or somewhat
GM foods A research poll in 2018 with 2537 adult participants asked whether GM foods are better or worse for one’s health.Here is how they responded:Responses Number Worse 1249 Neither Better nor Worse 1123 Better 134 No Answer 31 Total 2537 If we select a respondent at random from this sample of
Shootings A poll in December 2015 asked the respondents of a country whether they were worried if someone in their family would become a victim of a mass shooting. The poll asked 1028 adults to classify their worry between “very worried,”“somewhat worried,” “not too worried,” and “not
Final project You used the Multiplication Rule to calculate probabilities about the calculus background of your statistics groupmates in Exercise 30.a) What must be true about the groups in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
Repairs again You use the multiplication rule and, sometimes, the addition rule to calculate repair probabilities in Exercise 29.a) What must be true about your cars in order to make use of the multiplication rule valid?b) Do you think this assumption is reasonable? Explain.
Another project You are assigned to be part of a group of three students from the intro stats class described in Exercise 28.What is the probability that of your other two groupmates,a) neither has studied calculus?b) both have studied at least one semester of calculus?c) at least one has had more
If you own three cars, use both multiplication rule and addition rule to find the probability that:a) none will need repair.b) all will need repair.c) two or more cars will need repair.
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