Question 1

Which one of the following probability distributions accurately represents the random variable "the number of times heads comes up in two tosses of a fair coin"?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which one of the following probability distributions...

Question 2

Seven percent of the potential customers visiting Gadget.com's website make at least one purchase: 4% purchase item A, 5% purchase item B, and 2% percent purchase both.If you define "number of items purchased by a website visitor" as a random variable, the possible values for the random variable are, in ascending order,
A)1,2,3
B)2,4,5
C)0,1,2
D)1,1,1
E)3,2,1

Accepted Answer

The random variable "number of items purchased by a website visitor" can take on the values 0 (no purchase), 1 (purchase of either item A or B but not both), or 2 (purchase of both items A and B). This accounts for all possible outcomes given the percentages provided.

Question 3

Hi-Plains Design is bidding on a project that will earn the company at least $650 million.The competitive bidding process will involve presenting the company's proposal to three successive review panels at the client company, all of which must approve the proposal for Hi-Plains bid to be successful.If the proposal is approved by the first panel, Hi-Plains will present the proposal to the next panel.If it is approved there, Hi-Plains will present the proposal to the third panel.Hi-Plains estimates that its proposal has a 40% chance of approval at each of the stages.Define "number of Hi-Plains presentations" as your random variable for this "experiment." The possible values for the random variable (in ascending order) are:
A)0,1,2,3
B)1,2,3
C)0,1,2,3,4
D)1,2,3,4
E)0,1

Accepted Answer

The random variable "number of Hi-Plains presentations" can take values 1, 2, or 3, corresponding to the number of panels the proposal is presented to before either being rejected or fully approved.

Question 4

One of the conditions for a Poisson experiment is the need to assess probability for the number of occurrences of some event per unit .
A)space
B)time
C)distance
D)space, time, or distance
E)space or time

Accepted Answer

The Poisson distribution can be used to assess the probability of a given number of events occurring in a fixed interval of space, time, or distance.

Question 5

You need to buy three books for your finance course this semester.You estimate that there is 60% chance of that you can buy any one of the books cheaper online than in the bookstore.If you define "number of the finance books that will be cheaper online" as a random variable, the possible values for the random variable are, in ascending order:
A)1,2,3,4
B)0,1,2
C)2,4,6
D)0,1,2,3
E)4,3,2,1

Accepted Answer

The random variable represents the number of books that can be bought cheaper online. Since you are buying three books, the possible outcomes range from finding none (0) cheaper online to finding all three (3) cheaper online. Thus, the correct set of values is 0, 1, 2, 3.

Question 6

The step involved in building a discrete probability distribution is identifying the values for the random variable.
A)first
B)second
C)third
D)fourth
E)fifth

Accepted Answer

The answer of The step involved in building a discrete...

Question 7

Below is a table showing the probability distribution for the random variable x.Compute the expected value of the random variable. 
A)36.4
B)35.0
C)32.9
D)41.3
E)38.0

Accepted Answer

The answer of Below is a table showing the probability...

Question 8

You need to buy three books for your finance course this semester.You estimate that there is 60% chance of that you can buy any one of the books cheaper online than in the bookstore.If you define "number of the finance books that will be cheaper online" as a random variable, which set of probabilities would be used to form the probability distribution for this random variable?
A).064, .298, .422, .216
B).064, .288, .432, .216
C).064, .268, .452, .216
D).064, .238, .482, .216
E).238, .064, .216, .482

Accepted Answer

The probability distribution for the random variable, which represents the number of finance books that will be cheaper online, can be calculated using the binomial distribution formula: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n=3$ (the number of trials/books), $p=0.6$ (the probability of success, i.e., finding a cheaper book online), and $k$ is the number of successes (books found cheaper online). Calculating for $k=0, 1, 2, 3$, we get:- For $k=0$: $P(X=0) = \binom{3}{0}(0.6)^0(0.4)^3 = 1 \times 1 \times 0.064 = 0.064$- For $k=1$: $P(X=1) = \binom{3}{1}(0.6)^1(0.4)^2 = 3 \times 0.6 \times 0.16 = 0.288$- For $k=2$: $P(X=2) = \binom{3}{2}(0.6)^2(0.4)^1 = 3 \times 0.36 \times 0.4 = 0.432$- For $k=3$: $P(X=3) = \binom{3}{3}(0.6)^3(0.4)^0 = 1 \times 0.216 \times 1 = 0.216$Thus, the correct set of probabilities is 0.064, 0.288, 0.432, 0.216, which matches option B.

Question 9

The following probability distribution represents the number of vehicles available for use by a randomly selected US household.To simplify matters, the category "three or more" is replaced by "3" (Source: US Census, American FactFinder).Calculate the expected value of the number of vehicles available per household. 
A)0.25
B)0.42
C)1.50
D)1.66
E)2.50

Accepted Answer

The answer of The following probability distribution represents the number...

Question 10

The of a binomial distribution is equal to n time p.
A)expected value
B)variance
C)standard deviation
D)probability of success
E)the number of trials

Accepted Answer

The expected value (mean) of a binomial distribution is equal to the number of trials (n) multiplied by the probability of success (p), which is denoted as np.

Question 11

The number of re-tweets of your Twitter tweets over the last ten days is shown below.If you define a random variable that counts the number of daily re-tweets during this 10-day period, which set of probabilities would be used to form the probability distribution for this random variable? 3, 1, 1, 0, 1, 1, 2, 2, 0, 2.
A).1, .3, .5, .1
B).3, .4, .3, .1
C).2, .1, .5, .2
D).2, .4, .3, .1
E).2, .2, .4, .2

Accepted Answer

The probabilities are calculated based on the frequency of each number of re-tweets: 0 re-tweets (2 times), 1 re-tweet (4 times), 2 re-tweets (3 times), and 3 re-tweets (1 time). The probabilities are 0.2, 0.4, 0.3, and 0.1 respectively.

Question 12

Below is a table showing the probability distribution for the random variable x.Compute the variance of the random variable. 
A)84.2
B)72.0
C)54.2
D)64.0
E)95.9

Accepted Answer

The answer of Below is a table showing the probability...

Question 13

The calculations for the expected value (mean) and variance of a discrete probability distribution are essentially identical to those for a :
A)frequency distribution
B)percent frequency distribution
C)relative frequency distribution
D)binomial probability distribution
E)continuous probability distribution

Accepted Answer

The expected value and variance calculations for a discrete probability distribution are similar to those for a relative frequency distribution, as both involve probabilities or relative frequencies summing to 1.

Question 14

Below is a table showing the probability distribution for the random variable x.Compute the standard deviation of the random variable. 
A)8.49
B)14.63
C)8.00
D)3.85
E)23.56

Accepted Answer

The answer of Below is a table showing the probability...

Question 15

Seven percent of the potential customers visiting Gadget.com's website make at least one purchase: 4% purchase item A, 5% purchase item B, and 2% percent purchase both.If you define "number of items purchased by a website visitor" as a random variable, which set of probabilities would be used to form the probability distribution for this random variable?
A).63, .25, .12
B).82, .12, .05
C).93, .05, .02
D).83, .14, .03
E).12, .23, .65

Accepted Answer

The answer of Seven percent of the potential customers visiting...

Question 16

Hi-Plains Design is bidding on a project that will earn the company at least $650 million.The competitive bidding process will involve presenting the company's proposal to three successive review panels at the client company, all of which must approve the proposal for Hi-Plains bid to be successful.If the proposal is approved by the first panel, Hi-Plains will present the proposal to the next panel.If it is approved there, Hi-Plains will present the proposal to the third panel.Hi-Plains estimates that its proposal has a 40% chance of approval at each of the stages.Define "number of review panel approvals" as your random variable.The possible values for the random variable (in ascending order) are:
A)1,2,3
B)1,2,3,4
C)0,1,2
D)2,3,4
E)0,1,2,3

Accepted Answer

The random variable "number of review panel approvals" can take on values from 0 (if the proposal is rejected at the first panel) to 3 (if the proposal is approved by all three panels), inclusive.

Question 17

The number of re-tweets of your Twitter tweets over the last ten days is shown below.If you pick a day at random, how likely is it that the number of re-tweets on that day is 2? 3, 1, 1, 0, 1, 1, 2, 2, 0, 2.
A).10
B).30
C).20
D).25
E).40

Accepted Answer

The answer of The number of re-tweets of your Twitter...

Question 18

Which one of the following probability distributions represents the random variable "the number of 6's that appear in a roll of two fair dice"?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which one of the following probability distributions...

Question 19

Hi-Plains Design is bidding on a project that will earn the company at least $650 million.The competitive bidding process will involve presenting the company's proposal to three successive review panels at the client company, all of which must approve the proposal for Hi-Plains' bid to be successful.If the proposal is approved by the first panel, Hi-Plains will present the proposal to the next panel.If it is approved there, Hi-Plains will present the proposal to the third panel.Hi-Plains estimates that its proposal has a 40% chance of approval at each of the stages.Define "number of panels that fail to approve the proposal" as your random variable.The possible values for the random variable (in ascending order) are:
A)0,1,2,3
B)1,2
C)1,2,3,4
D)0,1
E)0,0,2,3

Accepted Answer

The answer of Hi-Plains Design is bidding on a project...

Question 20

The number of re-tweets of your Twitter tweets over the last ten days is shown below.If you define a random variable that counts the number of daily re-tweets during this 10-day period, show the possible values for the random variable in ascending order. 3, 1, 1, 0, 1, 1, 2, 2, 0, 2.
A)0, 1, 2, 3
B)1, 2, 3, 4
C)1, 1, 0, 3
D)2, 2, 1, 0
E)0, 2, 3, 4

Accepted Answer

The possible values for the random variable, which counts the number of daily re-tweets, are the unique numbers in the given data set, sorted in ascending order: 0, 1, 2, 3.

Quiz 5: Discrete Probability Distributions

Which one of the following probability distributions accurately represents the random variable "the number of times heads comes up in two tosses of a fair coin"?

One of the conditions for a Poisson experiment is the need to assess probability for the number of occurrences of some event per unit .

The step involved in building a discrete probability distribution is identifying the values for the random variable.

Below is a table showing the probability distribution for the random variable x.Compute the expected value of the random variable.

The of a binomial distribution is equal to n time p.

Below is a table showing the probability distribution for the random variable x.Compute the variance of the random variable.

The calculations for the expected value (mean) and variance of a discrete probability distribution are essentially identical to those for a :

Below is a table showing the probability distribution for the random variable x.Compute the standard deviation of the random variable.

The number of re-tweets of your Twitter tweets over the last ten days is shown below.If you pick a day at random, how likely is it that the number of re-tweets on that day is 2? 3, 1, 1, 0, 1, 1, 2, 2, 0, 2.

Which one of the following probability distributions represents the random variable "the number of 6's that appear in a roll of two fair dice"?

The number of re-tweets of your Twitter tweets over the last ten days is shown below.If you define a random variable that counts the number of daily re-tweets during this 10-day period, show the possible values for the random variable in ascending order. 3, 1, 1, 0, 1, 1, 2, 2, 0, 2.