Question 1

Approximately 1% of all USPS package deliveries are lost.You select 10 deliveries at random.Assuming that all the binomial conditions are met, what is the "expected" number of lost packages in this 10 delivery sample?

Accepted Answer

A) 1.00 
B) .1542 
C) .0666 
D) .100 
E) .0914

Question 2

The expected value of a discrete random variable is the average value for the random variable over many repeats of the experiment.

Accepted Answer

A) True 
 B)False

Question 3

Use the Poisson probability function to find P(3 < x < 5), where λ = 2.

Accepted Answer

A) .2497 
B) .3067 
C) .1961 
D) .1789 
E) .4282

Question 4

The following probability distribution represents the number of bedrooms in a randomly selected US household.To simplify matters, the category "five or more" is replaced by "5" (Source: US Census, American FactFinder).Calculate the variance of the number of bedrooms per household.

Accepted Answer

A) 0.017 
B) 1.070 
C) 1.145 
D) 2.917 
E) 3.215

Question 5

The binominal distribution:

Accepted Answer

A) may be used to describe a discrete or a continuous random variable. 
B) is used to describe a particular type of discrete random variable. 
C) is a special case of the Poisson distribution. 
D) may be used to describe any experiment whose outcome takes discrete values. 
E) is only useful when dealing with distance, time, or space.

Question 6

Which of the following is a condition of a binomial experiment?

Accepted Answer

A) only two outcomes are possible on each of the trials 
B) the trials are statistically independent 
C) the probability of success remains constant throughout the experiment 
D) all of the above 
E) none of the above

Question 7

The expected value of a discrete random variable is the value of the random variable that occurs most frequently.

Accepted Answer

A) True 
 B)False

Question 8

Which of the following best describes the logic of the binomial function?

Accepted Answer

A) the first part counts the number of ways in which exactly x successes in n trials can occur while the second part computes the probability of each of the ways in which the x successes can occur 
B) the first part counts the number of ways in which exactly n successes in x trials can occur while the second part computes the probability of each of the ways in which the n successes can occur 
C) the first part computes the probability of each of the ways in which the x successes can occur while the second part simply counts the number of ways in which exactly x successes in n trials can occur 
D) the first part computes the probability of each of the ways in which the n successes can occur while the second part simply counts the number of ways in which exactly n successes in x trials can occur 
E) none of the above

Question 9

Use the Poisson probability function to find P(x > 13), where λ = 5.

Accepted Answer

A) .0002 
B) .0004 
C) .0200 
D) .0168 
E) .0001

Question 10

The symbol "x" is used to denote the random variable while the symbol "P(x)" is used to denote the probabilities associated with the random variable.

Accepted Answer

A) True 
 B)False

Question 11

On average, 2.3 wind turbines at the vast Kindler Range Wind Farm malfunction and need repair.Assume that all the Poisson conditions are met.Letting x represent values of the random variable "number of turbines that malfunction during any one day," determine the probability that x = 2.

Accepted Answer

A) .1578 
B) .2652 
C) .2231 
D) .3472 
E) .3225

Question 12

Use the Binomial distribution to produce P(x < 12), where n = 15, p = .7.

Accepted Answer

A) .7821 
B) .6631 
C) .5978 
D) .8116 
E) .8732

Question 13

At work, Serge receives an average of four e-mails every hour.Assuming that all of the Poisson conditions are met, use the Poisson probability function to calculate the probability that Serge receives no e-mails in the next hour.

Accepted Answer

A) 0% 
B) 2% 
C) 18% 
D) 25% 
E) 44%

Question 14

Car Sounds sells and installs high-end sound systems for cars.10% of the systems that the company installs need to be re-installed because of faulty first-time installation.You plan to randomly select 20 of Car Sounds' recent installations.How likely is it that the company will have to re-install no more than one of these systems?

Accepted Answer

A) .2671 
B) .3416 
C) .2956 
D) .3687 
E) .3918

Question 15

Car Sounds sells and installs high-end sound systems for cars.10% of the systems that the company installs need to be re-installed because of faulty first-time installation.You plan to randomly select 20 of Car Sounds' recent installations.How likely is it that at least three of these systems will require re-installation.?

Accepted Answer

A) .3230 
B) .3732 
C) .2554 
D) .1989 e .2868

Question 16

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.

Accepted Answer

A) .10 
B) .30 
C) .20 
D) .25 
E) .40

Question 17

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:

Accepted Answer

A) 0,1,2,3 
B) 1,2,3 
C) 0,1,2,3,4 
D) 1,2,3,4 
E) 0,1

Question 18

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 standard deviation of the number of vehicles available per household.

Accepted Answer

A) 0.11 
B) 0.79 
C) 0.89 
D) 1.12 
E) 1.45

Question 19

For a binomial distribution, find P(x = 2), where n = 8, p = .7.

Accepted Answer

A) .0100 
B) .0467 
C) .0217 
D) .0952 
E) .1361

Question 20

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:

Accepted Answer

A) 0,1,2,3 
B) 1,2 
C) 1,2,3,4 
D) 0,1 
E) 0,0,2,3

Exam 5: Discrete Probability Distributions

Approximately 1% of all USPS package deliveries are lost.You select 10 deliveries at random.Assuming that all the binomial conditions are met, what is the "expected" number of lost packages in this 10 delivery sample?

The expected value of a discrete random variable is the average value for the random variable over many repeats of the experiment.

Use the Poisson probability function to find P(3 < x < 5) , where λ = 2.

The following probability distribution represents the number of bedrooms in a randomly selected US household.To simplify matters, the category "five or more" is replaced by "5" (Source: US Census, American FactFinder) .Calculate the variance of the number of bedrooms per household.

The binominal distribution:

Which of the following is a condition of a binomial experiment?

The expected value of a discrete random variable is the value of the random variable that occurs most frequently.

Which of the following best describes the logic of the binomial function?

Use the Poisson probability function to find P(x > 13) , where λ = 5.

The symbol "x" is used to denote the random variable while the symbol "P(x)" is used to denote the probabilities associated with the random variable.

On average, 2.3 wind turbines at the vast Kindler Range Wind Farm malfunction and need repair.Assume that all the Poisson conditions are met.Letting x represent values of the random variable "number of turbines that malfunction during any one day," determine the probability that x = 2.

Use the Binomial distribution to produce P(x < 12) , where n = 15, p = .7.

At work, Serge receives an average of four e-mails every hour.Assuming that all of the Poisson conditions are met, use the Poisson probability function to calculate the probability that Serge receives no e-mails in the next hour.

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.

For a binomial distribution, find P(x = 2) , where n = 8, p = .7.