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# Finite math final | Mathematics homework help

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### 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.

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### 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.

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

x-5-10158P(X = x)0.110.170.280.230.110.1

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### 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?

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

Find the event EFG.

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### 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?

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### 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?

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### 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 . Are E and F dependent events?
a., yes

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### 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?

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### 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 )

a.P ( Z < 1.37 ) = 0.9147

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### 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 )

a.P (- 1.36 < Z < 1.75 ) = 0.8730

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### 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?

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### 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

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### 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)​​​​​​​

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### 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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