Question 1: Suppose A Probability Distribution Of A Random V

Question 1suppose A Probability Distribution Of A Random Variable xi R

QUESTION 1 Suppose 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.

QUESTION 2 Human 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- }

QUESTION 3 A 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.dependent

b.independent

QUESTION 4 Determine whether the table gives the probability distribution of the random variable X. Explain your answer.

x	P( X = x )
0	0.11
1	0.17
2	0.28
3	0.23
4	0.11
5	0.1

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.

QUESTION 5 A 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 week, 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}

QUESTION 6 Find the expected value of a random variable X having the following probability distribution: x - P ( X = x ) 0.1 0.17 0.28 0.23 0.11 0.1

a. E ( X ) = 0.73

b. E ( X ) = 0.86

c. E ( X ) = 0.79

d. E ( X ) = 1.07

QUESTION 7 The 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 incorrect

b.The statement is correct

QUESTION 8 The 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.71

b.80

c.82

d.89

e.86

QUESTION 9 An 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 )}

QUESTION 10 In 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. cents

b. cents

c. cents

d. cents

e. cents

QUESTION 11 Let Z be the standard normal variable. Find the value of z if z satisfies .

a. .

b. .

c. .

d. .

e. .

QUESTION 12 In ''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.0.0024

b.0.0017

c.0.0004

d.1

e.0.0002

f.0

QUESTION 13 Suppose X is a normal random variable with and . Find the value of .

a.0.8996

b.0.8945

c.0.8818

d.0.9857

e.0. points

QUESTION 14 The grade distribution for a certain class is shown in the table. Find the probability distribution associated with these data.

Grade	Frequency of Occurrence
A	48
B	20
C	62

a.Grade ABCDF Frequency of0.1 0.21 0.48 0.16 0.05 Occurrence

b.Grade ABCDF Frequency of0.11 0.2 0.43 0.15 0.11Occurrence

c.Grade ABCDF Frequency of0.10 0.15 0.45 0.2 0.1Occurrence

d.Grade ABCDF Frequency of0.1 0.2 0.5 0.15 0.05Occurrence

QUESTION 15 One of the key determinants of economic growth is access to capital. Using 54 variables to create an index of 1-7, with 7 being best possible access to capital, Milken Institute 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: Country Hong Kong Netherlands U.K. Singapore Switzerland U.S.Australia Finland Germany Denmark Index 5.59 5.07 5.04 5.47 5.23 5.39 5.92 5.01 5.27 5.43 Find the mean of the indices of the top ten nations. What is the standard deviation of these data?

a.μ = 3.32; σ = 0.43

b.μ = 5.94; σ = 0.27

c.μ = 5.34; σ = 0.58

d.μ = 5.34; σ = 0.28

e.μ = 3.25; σ = 0.28

QUESTION 16 Let 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}

QUESTION 17 The following table gives the number of people killed in rollover crashes in various types of vehicles in 2002: Types of Vehicles Cars, Pickups, SUVs, Vans. Deaths. If 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.0.55

b.0.47

c.0.37

d.0.52

e.0.40

QUESTION 18 Give 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 discrete

c. 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 discrete

QUESTION 19 In 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 Service. Respondents: Has remained the same from two years ago (630), Has diminished over that time frame (413), Has improved over that time frame (329), Weren't sure (28). If 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.0.685

b.0.695

c.0.655

d.0.665

QUESTION 20 A 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 P(E ∩ F). Are E and F dependent events?

a. , yes

b. , no

c. , no

d. , yes

QUESTION 21 Let S be a sample space for an experiment and let E and C be events of this experiment. Show that the events E and C are mutually exclusive. 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.

QUESTION 22 There 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.

QUESTION 23 According 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: On ground, taxiing (5%), During takeoff (9%), Climbing to cruise altitude (20%), En route (4%), Descent and approach (31%), Landing (31%). If 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.

QUESTION 24 An 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.

QUESTION 25 Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. P ( Z

a. P ( Z

b. P ( Z

c. P ( Z

d. P ( Z

QUESTION 26 Let A and B be events in a sample space S such that , , and . Find: .

a.

b.

c.

d.

QUESTION 27 Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. P ( - 1.36

a. P (- 1.36

b. P (- 1.36

c. P (- 1.36

d. P (- 1.36

QUESTION 28 Let Z be the standard normal variable. Find the value of z if z satisfies .

a.

b.

c.

d.

e.

QUESTION 29 In 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%

QUESTION 30 A 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 is

b.The probability is

c.The probability is

d.The probability is

QUESTION 31 Among 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.0.69

b.0.30

c.0.43

d.0.56

e.0.82

QUESTION 32 Give the range of values that the random variable X may assume and classify the