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Questions and Answers of Statistics

Hours after the rigging of the Pennsylvania state lottery was announced on September 19, 1980, Connecticut state lottery officials were stunned to learn that their winning number for the day was
The American Journal of Sports Medicine published a study of 810 women collegiate rugby players with two common knee injuries: medial cruciate ligament (MCL) sprains and anterior cruciate ligament
Refer to Exercise 4.11. Suppose that there are six prospective jurors, four men and two women, who might be impaneled to sit on the jury in a criminal case. Two jurors are randomly selected from
An article in The American Journal of Sports Medicine compared the results of magnetic resonance imaging (MRI) evaluation with arthroscopic surgical evaluation of cartilage tears at two sites in the
Two men each toss a coin. They obtain a "match" if either both coins are heads or both are tails. Suppose the tossing is repeated three times. a. What is the probability of three matches? b. What is
Experience has shown that, 50% of the time, a particular union- management contract negotiation led to a contract settlement within a 2-week period, 60% of the time the union strike fund was adequate
Suppose the probability of remaining with a particular company 10 years or longer is 1/6. A man and a woman start work at the company on the same day. a. What is the probability that the man will
Accident records collected by an automobile insurance company give the following information: The probability that an insured driver has an automobile accident is .15; if an accident has occurred,
Suppose that at a particular supermarket the probability of waiting 5 minutes or longer for checkout at the cashier's counter is .2. On a given day, a man and his wife decide to shop individually at
A quality-control plan calls for accepting a large lot of crankshaft bearings if a sample of seven is drawn and none are defective. What is the probability of accepting the lot if none in the lot are
Only 40% of all people in a community favor the development of a mass transit system. If four citizens are selected at random from the community, what is the probability that all four favor the mass
A research physician compared the effectiveness of two blood pressure drugs A and B by administering the two drugs to each of four pairs of identical twins. Drug A was given to one member of a pair;
To reduce the cost of detecting a disease, blood tests are conducted on a pooled sample of blood collected from a group of n people. If no indication of the disease is present in the pooled blood
A food company plans to conduct an experiment to compare its brand of tea with that of two competitors. A single person is hired to taste and rank each of three brands of tea, which are unmarked
How many times should a coin be tossed to obtain a probability equal to or greater than .9 of observing at least one head?
A survey to determine the availability of flextime schedules in the California workplace provided the following information for 220 firms located in two California cities.A company is selected at
An experiment is run as follows-the colors red, yellow, and blue are each flashed on a screen for a short period of time. A subject views the colors and is asked to choose the one he feels was
A taste-testing experiment is conducted at a local supermarket, where passing shoppers are asked to taste two soft-drink samples-one Pepsi and one Coke-and state their preference. Suppose that four
A certain virus afflicted the families in three adjacent houses in a row of 12 houses. If houses were randomly chosen from a row of 12 houses, what is the probability that the three houses would be
The board of directors of a major symphony orchestra has voted to create a committee for the purpose of handling employee complaints. The committee will consist of the president and vice president of
Suppose that P(A) = .3 and P(B) = .4. a. If P(A ∩ B) = .12 are A and B independent? Justify your answer. b. If P(A ∪ B) .7 what is P(A ∩ B)? Justify your answer. c. If A and B are
The following information reflects the results of a survey reported by Mya Frazier in an Ad Age Insights white paper. Working spouses were asked "Who is the household breadwinner?" Suppose that one
Four equally qualified runners, John, Bill, Ed, and Dave, run a 100-meter sprint, and the order of finish is recorded. a. How many simple events are in the sample space? b. If the runners are equally
In a genetics experiment, the researcher mated two Drosophila fruit flies and observed the traits of 300 offspring. The results are shown in the table.One of these offspring is randomly selected and
Which of the following comes closest to your views on the origin and development of human beings? Do you believe that human beings have developed over millions of years from less advanced forms of
Evaluate the following permutations. a. P53 b. P109 c. P66 d. P201
A sample space S consists of five simple events with these probabilities:P(E1) = P(E2) = .15P(E3) = .4P(E4) = 2P(E5)a. Find the probabilities for simple events E4 and E5.b. Find the probabilities for
Evaluate these combinations: a. C53 b. C109 c. C66 d. C201
In how many ways can you select five people from a group of eight if the order of selection is important?
In how many ways can you select two people from a group of 20 if the order of selection is not important?
Three dice are tossed. How many simple events are in the sample space?
Four coins are tossed. How many simple events are in the sample space?
Three balls are selected from a box containing 10 balls. The order of selection is not important. How many simple events are in the sample space?
You own 4 pairs of jeans, 12 clean T-shirts, and 4 wearable pairs of sneakers. How many outfits (jeans, T-shirt, and sneakers) can you create?
A businessman in New York is preparing an itinerary for a visit to six major cities. The distance traveled, and hence the cost of the trip, will depend on the order in which he plans his route. How
Three students are playing a card game. They decide to choose the first person to play by each selecting a card from the 52-card deck and looking for the highest card in value and suit. They rank the
A sample space contains 10 simple events: E1, E2,... , E10. If P(E1) = 3P(E2) = .45 and the remaining simple events are equiprobable, find the probabilities of these remaining simple events.
Five cards are selected from a 52-card deck for a poker hand. a. How many simple events are in the sample space? b. A royal flush is a hand that contains the A, K, Q, J, and 10, all in the same suit.
Refer to Exercise 4.31. You have a poker hand containing four of a kind. a. How many possible poker hands can be dealt? b. In how many ways can you receive four cards of the same face value and one
A study is to be conducted in a hospital to determine the attitudes of nurses toward various administrative procedures. If a sample of 10 nurses is to be selected from a total of 90, how many
Two city council members are to be selected from a total of five to form a subcommittee to study the city's traffic problems. a. How many different subcommittees are possible? b. If all possible
Professional basketball is now a reality for women basketball players in the United States. There are two conferences in the WNBA, each with six teams, as shown in the table below.Two teams, one from
Refer to Exercise 4.14, in which a 100-meter sprint is run by John, Bill, Ed, and Dave. Assume that all of the runners are equally qualified, so that any order of finish is equally likely. Use the mn
A woman brought a complaint of gender discrimination to an eight-member human relations advisory board. The board, composed of five women and three men, voted 5-3 in favor of the plaintiff, the five
A student prepares for an exam by studying a list of 10 problems. She can solve 6 of them. For the exam, the instructor selects 5 questions at random from the list of 10. What is the probability that
A monkey is given 12 blocks: 3 shaped like squares, 3 like rectangles, 3 like triangles, and 3 like circles. If it draws three of each kind in order-say, 3 triangles, then 3 squares, and so on-would
A particular basketball player hits 70% of her free throws. When she tosses a pair of free throws, the four possible simple events and three of their associated probabilities are as given in the
An experiment can result in one of five equally likely simple events, E1, E2, . . . , E5. Events A, B, and C are defined as follows: A: E1, E3 P(A) = .4 B: E1, E2, E4, E5 P(B) = .8 C: E3, E4 P(C) =
Refer to Exercise 4.40. Use the definition of a complementary event to find these probabilities: a. P(Ac) b. P((A ∩ B)c) Do the results agree with those obtained in Exercise 4.40? Exercise 4.40 An
Refer to Exercise 4.40. Use the definition of conditional probability to find these probabilities: a. P(A | B) b. P(B | C) Do the results agree with those obtained in Exercise 4.40? Exercise 4.40 An
Refer to Exercise 4.40. Use the Addition and Multiplication Rules to find these probabilities: a. P(A ∪ B) b. P(A ∩ B) c. P(B ∩ C) Do the results agree with those obtained in Exercise
Refer to Exercise 4.40. a. Are events A and B independent? b. Are events A and B mutually exclusive? Exercise 4.40 An experiment can result in one of five equally likely simple events, E1, E2, . . .
Suppose P(A) = .1 and P(B) = .5.a. If P(A | B) = .1, what is P(A ∩ B)?b. If P(A | B) = .1, are A and B independent?c. If P(A ∩ B) = 0, are A and B independent?d. If P(A ∪ B) = .65, are A and B
An experiment consists of tossing a single die and observing the number of dots that show on the upper face. Events A, B, and C are defined as follows: A: Observe a number less than 4 B: Observe a
Refer to Exercise 4.46. a. Are events A and B independent? Mutually exclusive? b. Are events A and C independent? Mutually exclusive? Exercise 4.46. An experiment consists of tossing a single die and
Two fair dice are tossed. a. What is the probability that the sum of the number of dots shown on the upper faces is equal to 7? To 11? b. What is the probability that you roll "doubles"- that is,
Suppose that P(A) = .4 and P(B) = .2. If events A and B are independent, find these probabilities: a. P(A ∩ B) b. P(A ∪ B)
A jar contains four coins: a nickel, a dime, a quarter, and a half-dollar. Three coins are randomly selected from the jar.a. List the simple events in S.b. What is the probability that the selection
Suppose that P(A) = .3 and P(B) = .5. If events A and B are mutually exclusive, find these probabilities: a. P(A ∩ B) b. P(A ∪ B)
Suppose that P(A) = .4 and P(A ∩ B) = .12. a. Find P(B | A). b. Are events A and B mutually exclusive? c. If P(B) = .3, are events A and B independent?
An experiment can result in one or both of events A and B with the probabilities shown in this probability table:Find the following probabilities: a. P(A) b. P(B) c. P(A ˆ© B) d. P(A
Refer to Exercise 4.52.a. Are events A and B mutually exclusive? Explain.b. Are events A and B independent? Explain.Exercise 4.52An experiment can result in one or both of events A and B with the
Many companies are now testing prospective employees for drug use. However, opponents claim that this procedure is unfair because the tests themselves are not 100% reliable. Suppose a company uses a
Suppose a group of research proposals was evaluated by a panel of experts to decide whether or not they were worthy of funding. When these same proposals were submitted to a second independent panel
A study of drug offenders who have been treated for drug abuse suggests that the likelihood of conviction within a 2-year period after treatment may depend on the offender's education. The
Use the probabilities of Exercise 4.56 to show that these equalities are true:a. P(A ˆ© B) = P(A)P(B | A)b. P(A ˆ© B) = P(B)P(A | B)c. P(A ˆª B) = P(A) + P(B) - P(A
Two people enter a room and their birthdays (ignoring years) are recorded. a. Identify the nature of the simple events in S. b. What is the probability that the two people have a specific pair of
If n people enter a room, find these probabilities: A: None of the people have the same birthday B: At least two of the people have the same birthday Solve for a. n = 3 b. n = 4
On the first day of kindergarten, the teacher randomly selects 1 of his 25 students and records the student's gender, as well as whether or not that student had gone to preschool.a. How would you
A college student frequents one of two coffee houses on campus, choosing Starbucks 70% of the time and Peet's 30% of the time. Regardless of where she goes, she buys a cafe mocha on 60% of her
A certain manufactured item is visually inspected by two different inspectors. When a defective item comes through the line, the probability that it gets by the first inspector is .1. Of those that
A survey of people in a given region showed that 20% were smokers. The probability of death due to lung cancer, given that a person smoked, was roughly 10 times the probability of death due to lung
A smoke-detector system uses two devices, A and B. If smoke is present, the probability that it will be detected by device A is .95; by device B, .98; and by both devices, .94. a. If smoke is
In 1865, Gregor Mendel suggested a theory of inheritance based on the science of genetics. He identified heterozygous individuals for flower color that had two alleles (one r = recessive white color
During the inaugural season of Major League Soccer in the United States, the medical teams documented 256 injuries that caused a loss of participation time to the player. The results of this
Men and women often disagree on how they think about selecting a mate. Suppose that a poll of 1000 individuals in their twenties gave the following responses to the question of whether it is more
Two stars of the LA Lakers are very different when it comes to making free throws. ESPN.com reports that Kobe Bryant makes 85% of his free throw shots while Lamar Odum makes 62% of his free throws.5
Player A has entered a golf tournament but it is not certain whether player B will enter. Player A has probability 1/6 of winning the tournament if player B enters and probability 3/4 of winning if
A sample is selected from one of two populations, S1 and S2, with probabilities P(S1) = .7 and P(S2) = .3. If the sample has been selected from S1, the probability of observing an event A is P(A |
A bowl contains three red and two yellow balls. Two balls are randomly selected and their colors recorded. Use a tree diagram to list the 20 simple events in the experiment, keeping in mind the order
If an experiment is conducted, one and only one of three mutually exclusive events S1, S2, and S3 can occur, with these probabilities: P(S1) = .2 P(S2) = .5 P(S3) = .3 The probabilities of a fourth
A population can be divided into two subgroups that occur with probabilities 60% and 40%, respectively. An event A occurs 30% of the time in the first subgroup and 50% of the time in the second
City crime records show that 20% of all crimes are violent and 80% are nonviolent, involving theft, forgery, and so on. Ninety percent of violent crimes are reported versus 70% of nonviolent
A worker-operated machine produces a defective item with probability .01 if the worker follows the machine's operating instructions exactly, and with probability .03 if he does not. If the worker
Suppose that, in a particular city, airport A handles 50% of all airline traffic, and airports B and C handle 30% and 20%, respectively. The detection rates for weapons at the three airports are .9,
A particular football team is known to run 30% of its plays to the left and 70% to the right. A linebacker on an opposing team notes that the right guard shifts his stance most of the time (80%) when
Under the "no pass, no play" rule for athletes, an athlete who fails a course is disqualified from participating in sports activities during the next grading period. Suppose the probability that an
Medical case histories indicate that different illnesses may produce identical symptoms. Suppose a particular set of symptoms, which we will denote as event H, occurs only when any one of three
Suppose 5% of all people filing the long income tax form seek deductions that they know are illegal, and an additional 2% incorrectly list deductions because they are unfamiliar with income tax
Suppose that a certain disease is present in 10% of the population, and that there is a screening test designed to detect this disease if present. The test does not always work perfectly. Sometimes
Refer to Exercise 4.7. A ball is randomly selected from the bowl containing three red and two yellow balls. Its color is noted, and the ball is returned to the bowl before a second ball is selected.
Identify the following as discrete or continuous random variables: a. Total number of points scored in a football game b. Shelf life of a particular drug c. Height of the ocean's tide at a given
Identify the following as discrete or continuous random variables: a. Increase in length of life attained by a cancer patient as a result of surgery b. Tensile breaking strength (in pounds per square
A random variable x has this probability distribution:a. Find p(4). b. Construct a probability histogram to describe p(x). c. Find µ, Ïƒ2, and Ïƒ. d. Locate the interval
A random variable x can assume five values: 0, 1, 2, 3, 4. A portion of the probability distribution is shown here:a. Find p(3). b. Construct a probability histogram for p(x). c. Calculate the
Let x equal the number observed on the throw of a single balanced die. a. Find and graph the probability distribution for x. b. What is the average or expected value of x? c. What is the standard
Let x represent the number of times a customer visits a grocery store in a 1-week period. Assume this is the probability distribution of x:Find the expected value of x, the average number of times a
If you toss a pair of dice, the sum T of the numbers appearing on the upper faces of the dice can assume the value of an integer in the interval2 ≤ T ≤ 12.a. Find the probability distribution for
The proportion of adults (18 years or more) who admit to texting while driving is 47%.7 Suppose you randomly select three adult drivers and ask if they text while driving.a. Find the probability
A key ring contains four office keys that are identical in appearance, but only one will open your office door. Suppose you randomly select one key and try it. If it does not fit, you randomly select

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