Mathematics homework help
FINAL
math
Expert
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 .
a.
b.
c.
d.
e.
1 points
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-}
1 points
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
1 points
QUESTION 4
Determine 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 points
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 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
QUESTION 6
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
a.E( X) = 0.73
b.E( X) = 0.86
c.E( X) = 0.79
d.E( X) = 1.07
1 points
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
1 points
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
1 points
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)}
1 points
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
1 points
QUESTION 11
Let Z be the standard normal variable. Find the value of z if z satisfies .
a.
b.
c.
d.
e.
1 points
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.0.0002f.0
1 points
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.0.9050
1 points
QUESTION 14
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
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 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
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}
1 points
QUESTION 17
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?
a.0.55
b.0.47
c.0.37
d.0.52
e.0.40
1 points
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
1 points
