Finite Math Final

QUESTION 1Suppose a probability distribution of a random variable X is represented by the accompanying histogram. Shade that part of the histogram whose area gives the probability .a.b.c.d.e.1 pointsQUESTION 2Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor B antigen is present, the letter O is used. The presence or absence of the Rh antigen is indicated by the symbols + or -, respectively. Thus, if a blood specimen is classified as AB +, it contains the A and the B antigens as well as the Rh antigen. Similarly, O- blood contains none of the three antigens.Using this information, determine the sample space corresponding to the different blood groups.a.{ A+, B+, A-, B-, O+, O-}b.{ AB+, AB-, A+, B+, A-, B-, O+, O-, ABO-, AO+, AO-, BO+, BO-}c.{ AB+, AB-, AO+, BO+, AO-, BO-, O+, O-}d.{ AB+, AB-, O+, O-}e.{ AB+, AB-, A+, B+, A-, B-, O+, O-}1 pointsQUESTION 3A card is drawn from a well-shuffled deck of 36 playing cards. Let E denote the event that the card drawn is red and let F denote the event that the card drawn is a hearts. Determine whether E and F are dependent events.a.dependentb.independent1 pointsQUESTION 4Determine whether the table gives the probability distribution of the random variable X. Explain your answer.xP(X = x)a.Yes, the sum of the probability assigned to the value of the random variable X is equal to 1.b.No, the probability assigned to a value of the random variable X cannot be negative.c.No, the sum of the probability assigned to the value of the random variable X is greater than 1.d.No, the sum of the probability assigned to the value of the random variable X is less than 1.e.No, the sum of the probability assigned to the value of the random variable X is not equal to 1.1 pointsQUESTION 5A certain airport hotel operates a shuttle bus service between the hotel and the airport. The maximum capacity of a bus is 20 passengers. On alternate trips of the shuttle bus over a period of 1 wk, the hotel manager kept a record of the number of passengers arriving at the hotel in each bus.Describe the event E that a shuttle bus carried fewer than twelve passengers.a.{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}b.{0, 1, 2, 3, 4, 5, 6, 7}c.{0, 1, 2, 3, 4, 5, 6, 7, 8}d.{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}1 pointsQUESTION 6Find the expected value of a random variable X having the following probability distribution:x-5-10158P(X = x)0.110.170.280.230.110.1a.E( X) = 0.73b.E( X) = 0.86c.E( X) = 0.79d.E( X) = 1.071 pointsQUESTION 7The sample space associated with an experiment is given by . The events and are mutually exclusive. Hence, the events Ec and F c are mutually exclusive.a.The statement is incorrectb.The statement is correct1 pointsQUESTION 8The scores on an Economics examination are normally distributed with a mean of 74 and a standard deviation of 11. If the instructor assigns a grade of A to 10% of the class, what is the lowest score (rounded to the nearest integer) a student may have and still obtain an A?a.71b.80c.82d.89e.861 pointsQUESTION 9An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe an appropriate sample space for this experiment.a.{( H, 1), ( T, 2), ( H, 3), ( T, 4), ( H, 5), ( T, 6), ( T, 1), ( T, 4), ( T, 5), ( H, 6)}b.{( H, 1), ( H, 2), ( H, 3), ( H, 4), ( H, 5), ( H, 6), ( T, 1), ( T, 2), ( T, 3), ( T, 4), ( T, 5), ( T, 6)}c.{(1, 2, 3, 4, 5, 6), ( H, T)}d.{( H, H, H, H, H, H, T, T, T, T, T, T, 1, 2, 3, 4, 5, 6)}e.{(1, H, T), (2, H, T), (3, H, T), (4, H, T), (5, H, T), (6, H, T)}1 pointsQUESTION 10In a lottery, 4,000 tickets are sold for $1 each. One first prize of $2,000, 1 second prize of $800, 3 third prizes of $120, and 10 consolation prizes of $12 are to be awarded. What are the expected net earnings of a person who buys one ticket?a. centsb. centsc.   centsd. centse. cents1 pointsQUESTION 11Let Z be the standard normal variable. Find the value of z if z satisfies .a.b.c.d.e.1 pointsQUESTION 12In ”The Numbers Game,” a state lottery, four numbers are drawn with replacement from an urn containing the digits 0-9, inclusive. Find the probability of a ticket holder having the indicated winning ticket.All four digits in any order(including the other winning tickets)a.0.0024b.0.0017c.0.0004d.1e.0.0002f.01 pointsQUESTION 13Suppose X is a normal random variable with and . Find the value of .a.0.8996b.0.8945c.0.8818d.0.9857e.0.90501 pointsQUESTION 14The grade distribution for a certain class is shown in the table. Find the probability distribution associated with these data.GradeABCDFFrequency of Occurrence482062a. GradeABCDFFrequency of0.1 0.21 0.480.160.05 Occurrenceb.GradeABCDFFrequency of0.110.2 0.430.15 0.11Occurrencec. GradeABCDFFrequency of0.10.15 0.450.2 0.1Occurrenced.GradeABCDFFrequency of0.1 0.2 0.5 0.15 0.05Occurrence1 pointsQUESTION 15One of the key determinants of economic growth is access to capital. Using 54 variables to create an index of 1-7, with 7 been best possible access to capital, Milken Institue ranked the following as the top ten nations (although technically Hong Kong is not a nation) by the ability of their entrepreneurs to gain access to capital:CountryHong KongNetherlandU.K.SingaporeSwitzerlandU.S.AustraliaFinlandGermanyDenmarkIndex5.595.075.045.475.235.395.925.015.275.43Find the mean of the indices of the top ten nations. What is the standard deviation of these data?a.μ = 3.32; σ = 0.43b.μ = 5.94; σ = 0.27c.μ = 5.34; σ = 0.58d.μ = 5.34; σ = 0.28e.μ = 3.25; σ = 0.281 pointsQUESTION 16Let S = {1, 2, 3, 4, 5, 6}, E = {1, 3, 5}, F = {2, 4, 6} and G = {2, 3} .Find the event E ∪ F ∪ G.a.E ∪ F ∪ G = {2, 3, 4, 5, 7}b.E ∪ F ∪ G = {1, 2, 3, 4, 5, 6}c.E ∪ F ∪ G = {1, 3, 4, 5, 6}d.E ∪ F ∪ G = {1, 2, 3, 5, 6}1 pointsQUESTION 17The following table gives the number of people killed in rollover crashes in various types of vehicles in 2002:Types of VehiclesCarsPickupsSUVsVansDeaths472026602195684If a fatality due to a rollover crash in 2002 is picked at random, what is the probability that the victim was in a pickup or an SUV?a.0.55b.0.47c.0.37d.0.52e.0.401 pointsQUESTION 18Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous.X = The number of defective watches in a sample of four watches.a.X may assume the values of any positive integer. The random variable is continuous.b.{0,1,2,3,4,5,6,7,8,9}; The random variable is infinite discretec.X may assume the values of any positive integer. The random variable is infinite discrete.d.{0,1,2,3,4,5,6,7,8,9}; The random variable is finite discrete1 pointsQUESTION 19In a survey conducted in November 2002 of 1,400 international business travelers concerning in-flight service over the past few years, the following information was obtained.Comments on Quality of ServiceRespondentsHas remained the same from two years ago.630Has diminished over that time frame.413Has improved over that time frame.329Weren’t sure.28If a person in the survey is chosen at random, what is the probability that he or she has rated the in-flight service as remaining the same or improved over the time frame in question?a.0.685b.0.695c.0.655d.0.665e.0.6751 pointsQUESTION 20A pair of fair dice is cast. Let E denote the event that the number falling uppermost in the first die is 5 and let F denote the event that the sum of the numbers falling uppermost is 8.Compute . Are E and F dependent events?a., yesb., noc., nod., yes1 pointsQUESTION 21Let S be a sample space for an experiment and let E and C be events of this experiment. Show that the events and are mutually exclusive.Hint: Use De Morgan’s law.a.By De Morgan’s law,  ,  so the events are mutually exclusive.b.By De Morgan’s law, , so the events are mutually exclusive.c.By De Morgan’s law, , so the events are mutually exclusive.d.By De Morgan’s law, , so the events are mutually exclusive.e.By De Morgan’s law, , so the events are not mutually exclusive.1 pointsQUESTION 22There were 42 different presidents of the United States from 1789 through 2000. What is the probability that at least four of them had the same birthday?a.b.c.d.e.f.1 pointsQUESTION 23According to a study of Western-built commercial jets involved in crashes during ten years, the percent of airplane crashes that occur at each stage of flight are as follows:PhasePercentOn ground, taxiing5During takeoff9Climbing to cruise altitude20En route4Descent and approach31Landing31If one of the doomed flights during ten years is picked at random, what is the probability that it crashed while taxiing on the ground or while en route?a.b.c.d.1 pointsQUESTION 24An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event “A head is tossed and an even number is rolled.”a.b.c.d.1 pointsQUESTION 25Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve.P ( Z < 1.37 )a.P ( Z < 1.37 ) = 0.9147b.P ( Z < 1.37 ) = 0.9319c.P ( Z < 1.37 ) = 0.9082d.P ( Z < 1.37 ) = 1.00001 pointsQUESTION 26Let A and B be events in a sample space S such that , , and . Find: .a.b.c.d.1 pointsQUESTION 27Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve.P ( - 1.36 < Z < 1.75 )a.P (- 1.36 < Z < 1.75 ) = 0.8730b.P (- 1.36 < Z < 1.75 ) = 0.9599c.P (- 1.36 < Z < 1.75 ) = 0.0869d.P (- 1.36 < Z < 1.75 ) = 1.04681 pointsQUESTION 28Let Z be the standard normal variable. Find the value of z if z satisfies .a.b.c.d.e.1 pointsQUESTION 29In European roulette the wheel is divided into 37 compartments numbered 1 through 36 and 0. (In American roulette there are 38 compartments numbered 1 through 36, 0, and 00.) Find the expected value of the winnings on a $3 bet placed on red in European roulette. Round your answer to the nearest cent.a.$0.03%b.- $0.03%c.- $0.08%d.$0.08%1 pointsQUESTION 30A pair of fair dice is cast. What is the probability that the sum of the numbers shown uppermost is less than 6?a.The probability isb.The probability isc.The probability isd.The probability is1 pointsQUESTION 31Among 1,000 freshmen pursuing a business degree at a university, 520 are enrolled in an Economics course, 490 are enrolled in a Mathematics course, and 290 are enrolled in both an Economics and a Mathematics course.What is the probability that a freshman selected at random from this group is enrolled in exactly one of these two courses?a.0.69b.0.30c.0.43d.0.56e.0.821 pointsQUESTION 32Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous.X = The number of times an accountant takes the CPA examination before passinga.0 ≤ x < 24; continuousb.Any positive integer; infinite continuousc.Any integer; infinite discreted.0 ≤ x < ∞; continuouse.Any positive integer; infinite discrete1 pointsQUESTION 33The probability distribution of the random variable X is shown in the accompanying table:x- 5- 3- 2023 P ( X = x )0.120.140.330.150.110.15 Find , and .a.b.c.d.1 pointsQUESTION 34A survey was conducted by the Public Housing Authority in a certain community among 1,000 families to determine the distribution of families by size. The results follow.Family Size2345678Frequency of Occurrence3511962501236884Find the probability distribution of the random variable X, where X denotes the number of persons in a randomly chosen family.x2345678P(X = x)x2345678P(X = x)x2345678P(X = x)x2345678P(X = x)x2345678P(X = x)a. x2345678P(X = x)b. x2345678P(X = x)c. x2345678P(X = x)d. x2345678P(X = x)e. x2345678P(X = x)1 pointsQUESTION 35In a survey of 700 likely voters, the following question was asked: Do you support using cameras to identify red-light runners? The results of the survey follow:AnswerStrongly supportSomewhatsupportSomewhatopposeStronglyOpposeDon’tknowRespondents3201758011510What is the probability that a person in the survey selected at random favors using cameras to identify red-light runners?a.0.66b.0.71c.0.29d.0.611 pointsQUESTION 36If a sample of 8 batteries is selected from a lot of 11, of which 4 are defective, what is the expected number of defective batteries? Round your answer to next whole number.a.7b.10c.6d.12e.51 pointsQUESTION 37The results of recent television survey of American TV households revealed that 87 out of every 100 TV households have at least one remote control. What is the probability that a randomly selected TV household does not have at least one remote control?a.0.13b.0.23c.0.28d.0.87e.0.791 pointsQUESTION 38If a player placed a $8 bet on red and a $5 bet on black in a single play in American roulette, what would be the expected value of his winnings? Round your answer to the nearest cent.a. centsb. centsc. centsd. centse. cents1 pointsQUESTION 39The number of subscribers to five leading e-mail services is shown in the accompanying table:CompanyABCDESubscribers370,000150,000110,000100,00070,000Find the empirical probability distribution associated with these data.a. Company A B C D E Subscribers 0.4625   0.1875   0.1367   0.1254   0.0879b. Company A B C D E Subscribers 0.4609   0.1879   0.1379   0.1254   0.0879c. Company  A B C D E Subscribers 0.4625   0.1875   0.1375   0.125   0.0875d. Company A B C D E Subscribers 0.0875   0.125   0.1375   0.1875   0.46251 pointsQUESTION 40Maria sees the growth of her business for the upcoming year as being tied to the gross domestic product (GDP). She believes that her business will grow (or contract) at the rate of 5%, 4.5%, 3%, 0%, or - 0.5% per year if the GDP grows (or contracts) at the rate of between 2 and 2.5%, between 1.5 and 2%, between 1 and 1.5%, between 0 and 1%, and between - 1 and 0%, respectively.Maria has decided to assign a probability of 0.13, 0.24, 0.39, 0.19, and 0.05, respectively, to each outcome. At what rate does Maria expect her business to grow next year?a.3.005%b.2.615%c.2.325%d.2.875%

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