Finite math final | Mathematics homework help


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 ced2baa9 de83 47ef 9fe5 6041ef63d869.​
838bce6c 3592 4905 8b43 c0e03b07c77f
​a.​7aaf8d6f 1758 4e23 85d4 aca3ee3e03c6

b.17f9d806 d8e7 45ad b92b f373908b1e4e

c.bf8908b1 eb58 4e96 ab42 64787fc7f325

d.56fb9199 6329 4549 a101 4e1c50fe3c1a

e.59897de1 6e49 4464 b566 457c6dfa4a16

1 points   


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-}

1 points   


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.



1 points   


Determine whether the table gives the probability distribution of the random variable X. Explain your answer.
xbe21b86e 96cb 4977 a450 c2c57af34882cdb33b61 ac3b 493a bbe0 87c7d948dff183b2495e 2dd3 4d77 9a2d 2c7c8e202d37b57ed30d e5cf 48c7 b404 a3b45bdaa7e9dcaee90b de4c 483d a962 03d728a93bd3bd41239e d072 40b4 b048 26855c96f795P(X = x)eda89842 8848 4cb1 b672 58dd3d416ec90342c09a c2b8 4411 a6c7 c8b8d2d16d1fa3addadc debe 4a3a b02f 6395d822658de410cd95 4617 44d3 8535 e60975540c0b20d315a0 bb6a 49ce be93 f6c15e057c3555c7f6f8 2bc9 4f0c b91b 2beccbce30e1

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 points   


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 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 points   


Find the expected value of a random variable X having the following probability distribution:

x-5-10158P(X = x)

a.E( X) = 0.73

b.E( X) = 0.86

c.E( X) = 0.79

d.E( X) = 1.07

1 points   


The sample space associated with an experiment is given by 0054533c 8deb 43b7 9ac5 071d0e92f92b. The events 66d3e024 bca7 4dcf b0a6 6954763e3e22 and c504165b de16 48db 9560 b504270c6f47 are mutually exclusive. Hence, the events Ec and F c are mutually exclusive.

​a.The statement is incorrect

b.The statement is correct

1 points   


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?






1 points   


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)}

1 points   


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.25106693 1e70 45e3 b105 b73c2a7a30cb cents

b.9a483121 17d0 45dd 9d63 0ece2d06d9d7 cents

c.348c6263 c3b4 4313 bdc8 01117e270c56   cents

d.e882d57e c5a2 4535 9fa3 e11f4bf0395e cents

e.75d80fee c26b 4f5b 8abf 2480c17f3dcf cents

1 points   


Let Z be the standard normal variable. Find the value of z if z satisfies dd404364 b39c 4660 bdb8 181ef336c39a.​

a.18cf7e37 eec9 4c4d bdf1 70e5d64c7eda

b.c00e2ad7 a477 423e 89a8 0b1edbb8c3d2

c.f1af55ec 4915 4daf 904c 57f752b1c96b

d.838998a9 9f3b 4c02 8cee 547c8419abf5

e.7c445d91 e350 4dbe 88f5 4353ef2cf1d0

1 points   


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)






1 points   


Suppose X is a normal random variable with 5c01df98 0cf3 43df a79f 966951ef5c07 and 7a9fd87d 0545 42d3 9c84 5cfe672cef46. Find the value of 8ca920ea 9834 4eaa 91b0 29e6f2b5a906.






1 points   


The grade distribution for a certain class is shown in the table. Find the probability distribution associated with these data.
GradeABCDFFrequency of Occurrence482062

​a.​GradeABCDFFrequency of0.1 0.21 0.480.160.05 Occurrence     

​b.GradeABCDFFrequency of0.110.2 0.430.15 0.11Occurrence     

​c.​GradeABCDFFrequency of0.10.15 0.450.2 0.1Occurrence     

​d.GradeABCDFFrequency of0.1 0.2 0.5 0.15 0.05Occurrence     ​

1 points   


One 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.AustraliaFinlandGermanyDenmarkIndex5.595.075.045.475.235.395.925.015.275.43
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

1 points   


Let S = {1, 2, 3, 4, 5, 6}, E = {1, 3, 5}, F = {2, 4, 6} and G = {2, 3} .

Find the event EFG.

a.EFG = {2, 3, 4, 5, 7}

b.EFG = {1, 2, 3, 4, 5, 6}

c.EFG = {1, 3, 4, 5, 6}

d.EFG = {1, 2, 3, 5, 6}

1 points   


The following table gives the number of people killed in rollover crashes in various types of vehicles in 2002:

Types of VehiclesCarsPickupsSUVsVansDeaths472026602195684

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?






1 points   


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

1 points   


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 ServiceRespondentsHas remained the same from two years ago.630Has diminished over that time frame.413Has improved over that time frame.329Weren’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?






1 points   


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 c3c5eac2 0281 4857 90c0 2c3ccfe52c4a. Are E and F dependent events?
a.e1872bb3 b674 49b1 ab63 42674997517f, yes

b.3a06e564 e564 4dfd 95c2 adb36197e2a4, no

c.931da5ba f0e2 4ae2 82c3 91bb2955a547, no

d.eb1ebd70 41ec 435e aad8 9eb4885eb747, yes

1 points   


Let S be a sample space for an experiment and let E and C be events of this experiment. Show that the events e18c35a8 1e63 4a15 9543 5a44c3e0de4e and 7a9d1c88 100d 4217 83cf 1b713437de23 are mutually exclusive.​
Hint: Use De Morgan’s law.
​a.By De Morgan’s law,  6c5778bd be5f 4e15 99cd 032af2e90e8c ,  so the events are mutually exclusive.

b.By De Morgan’s law, a919961c b8e6 4880 8101 66ea4ee22192, so the events are mutually exclusive.

c.By De Morgan’s law, c4a50192 165f 4953 8bd2 e976733c3f64, so the events are mutually exclusive.

d.By De Morgan’s law, cd89f29a f20a 40f2 9315 f8d1adefab46, so the events are mutually exclusive.

e.By De Morgan’s law, 2a416516 a94b 45c8 aeff 34e68154796f, so the events are not mutually exclusive.

1 points   


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.65e22bac 7963 4657 9654 83435cfdbf86

b.a802067a 67c5 44b0 b8ef 8e76487f327e

c.2503ffac cf60 46d2 8dbe 21a8d75cc17f

d.291e1876 80f6 459e 94fd 1e2ffaf381d5

e.57d1ff71 67b3 451f 8be3 18dbb2f21dbb

f.fc2c4734 24f6 4c30 b9da c9d61a18fde2

1 points   


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 as follows:

PhasePercentOn ground, taxiing5During takeoff9Climbing to cruise altitude20En route4Descent and approach31Landing31
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.2e787f0b 7b00 4212 aeda 1cfba99fb13f

b.e7cb0e92 a4ca 4479 9276 78030dd0a8b1

c.a7845fd6 54e2 4ac6 bd21 7420b12ec634

d.eb6dfd79 a14e 4206 a69f a347b546d4ba

1 points   


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.b39fae1f 600d 4d13 81ee c42d2094271f

b.65977df9 e295 4dbe a3bf ded1271c936e

c.d4901d61 60d5 4efe a1cf df56bb5b8958

d.a215b5c0 e745 4cde 9ea8 b98f380ef7c5

1 points   


Find 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 )

e8afd07d f320 458d b6f6 ea97b1e88a57
a.P ( Z < 1.37 ) = 0.9147

b.P ( Z < 1.37 ) = 0.9319

c.P ( Z < 1.37 ) = 0.9082

d.P ( Z < 1.37 ) = 1.0000

1 points   


Let A and B be events in a sample space S such that bc0be6e3 9308 494f a5a9 088819a745d5, 30725cb9 bb79 4721 ba91 60c3ae221205, and 3bea47d8 f11d 4a81 9875 a9b90e704dcf. Find: 3799a288 f90a 499b a58a 3be9a44de760.​

a.812f7947 45d2 4c6a acfc 8e9f85511e97

b.b427da8b 8aef 4fb0 a894 fb194c86ca73

c.d1391cfd 0b12 4d0c 8e47 0f7a83740578

d.75b3b3d3 ab51 4187 b170 148e28505719

1 points   


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 < Z < 1.75 )

2301e556 4743 44ba b89d 938289619c6f
a.P (- 1.36 < Z < 1.75 ) = 0.8730

b.P (- 1.36 < Z < 1.75 ) = 0.9599

c.P (- 1.36 < Z < 1.75 ) = 0.0869

d.P (- 1.36 < Z < 1.75 ) = 1.0468

1 points   


Let Z be the standard normal variable. Find the value of z if z satisfies de3f7801 77f1 41fc 8365 2e8aa2288de3.
a.70b75044 1015 4e17 9b75 5350230ad2f1

b.c06ab250 5426 4a94 aa99 af901caae086

c.0887ac41 983d 43de ac8a e7901d7756d7

d.b4aa0c73 4c85 49a8 87aa db696e2e4d04

e.f27a601f db0f 4359 aa27 ec6c389fdc44

1 points   


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.


b.- $0.03%

c.- $0.08%


1 points   


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 1f7cf412 ec2b 4c00 b859 5d955a769f38

b.The probability is  967f781a 8c24 4593 978d 3821f1cdcd1e

c.The probability is  6d4802c4 800c 496a 8fb8 1991794c451a

d.The probability is  972e71ec da76 4dd2 9059 c9e34083b811

1 points   


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?






1 points   


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 times an accountant takes the CPA examination before passing

a.0 ≤ x < 24; continuous

b.Any positive integer; infinite continuous

c.Any integer; infinite discrete

d.0 ≤ x < ∞; continuous

e.Any positive integer; infinite discrete

1 points   


The probability distribution of the random variable X is shown in the accompanying table:
 x– 5- 3- 2023 P ( X = x ) Find 0292bc18 51ad 46db bb83 e064a0ecd285, 9dcf1c5a 7c21 4d1c b137 99eb40387d71 and 93215530 2e19 4f24 8f17 2ca3caf32159.

a.ff2558c1 1d6c 4805 9b2e 15ad0d887793b42d88ee 56d6 4350 8276 2c793e992900
0f3b1099 b7cb 42c4 a567 e6ffdcb14fde

b.d659d4b1 270e 4094 af84 079311099361a69638bd 1644 413b aef6 e8e07621368b
0f3b1099 b7cb 42c4 a567 e6ffdcb14fde

c.c5c538a9 7e47 466a ac36 f589da3f7f2ef8f79511 0e1b 47ea be4a f22aefd2c959
0f3b1099 b7cb 42c4 a567 e6ffdcb14fde

d.015320d9 6369 42cf 9184 a467a2d6f5c724c2d38c d3f8 4145 9b65 c12de616f272
0f3b1099 b7cb 42c4 a567 e6ffdcb14fde

1 points   


A 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)​946af5c4 f2ec 44bc a781 5ddb6f293f27ed9747db d2f1 4a29 b2e9 4372c92f1783d7fd6f78 7f5d 4581 933c 161e8f8303b7a371201e ba78 4221 bd6c fbd38e85a04ecce5cc4a a4d8 4365 8a4d cb17eb134b3f572876e9 92b4 4dc8 9236 70699294a1634135ebfd 178f 4460 beaf 592630d50a5e

b.​x2345678P(X = x)​8a211b17 3cb6 45e5 a8d8 35d970868aec7277a97c 392c 4d42 a736 f0708f51a68828dac6fd 0781 4ba3 9a36 9241ab7c396550093ac9 d1c9 47f5 ad0e be193898cb9c537a068b 74a8 4104 bda2 805b3da6b5e0519b1e4e 75db 44c6 8214 724d218055240d296a22 3822 4c34 9d80 1ad37d4eced3

c.​x2345678P(X = x)​a450c00d 2836 44d8 80a3 044231b337b0142d7ac4 834a 4c1e 8fdd 1839374e4f0bd2fb6101 602d 4db2 8d88 515a9f9c64fdc1922650 40a3 442b afcd a129426fc591492a6950 04c0 4856 aa47 8c8439e1ff02eda9459a 3d25 4be1 b234 b98569e13412a62cc238 996b 4d8a 8349 893b576dab31

d.​x2345678P(X = x)​fca01795 0712 4185 8378 9397dc523015ef44b343 a1c3 42e2 a82a 4dde5bd8f17aefd79433 9716 4bf0 a90e 91182561793106028a5a 776d 4705 8449 dcea71de965a629e2a67 c6c3 4ae0 bd4b 17f9cd192335af469878 8708 472f aca7 35f3978dada3e7138b45 0d82 44b9 8abe 412e3c2e9078

e.​x2345678P(X = x)​609e196d 319d 4d59 80bf 0a9ae1da4d5eff2c1671 2839 42ee b8fd d88c80698b9439fdbb9f 512f 416f 90c5 367d6e64f99a342eb062 c878 436f b0a2 82978e09fbdef0487f65 2410 4dfd be05 6346dade8f390a9140c9 f3a4 4b18 be27 ae005e95fa7fcc334545 d28c 4ca8 983d eaba29bbd848

1 points   


In 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 supportSomewhat
What is the probability that a person in the survey selected at random favors using cameras to identify red-light runners?





1 points   


If 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.






1 points   


The 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?






1 points   


If 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.e5c87d38 a7d8 48ec a052 349b78372e9e cents

b.f38d5f21 4ac2 40b6 9561 0f687aabf90b cents

c.3a896c8e cefa 49de ad4c ef6c0ac8aff0 cents

d.920f136f 28e2 4fd5 a48f 29e403161282 cents

e.54df53d0 a906 4bd5 af6e bfb5ca98e6c7 cents

1 points   


The 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   0.0879   ​
​b.​Company A B C D E Subscribers 0.4609   0.1879   0.1379   0.1254   0.0879   ​
​c.​Company ​A ​B C D E Subscribers 0.4625   0.1875   0.1375   0.125   0.0875   ​
​d.​Company A B C D E Subscribers 0.0875   0.125   0.1375   0.1875   0.4625 ​

1 points   


Maria 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?





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