Question 1

The mean of the binomial distribution is np(1-p).

Accepted Answer

False

Question 2

A Poisson random variable is a continuous variable that can be used to describe the number of occurrences of an event over a specified interval of time or space.

Accepted Answer

A Poisson random variable is a discrete variable, not a continuous variable.

Question 3

In a binomial experiment,the results of one trial are dependent on the results of other trials.

Accepted Answer

In a binomial experiment, each trial is independent of the other trials.

Question 4

The binomial distribution is characterized by situations that are analogous to
A)Drawing balls from and urn.
B)Coin tossing.
C)Counting defects on an item.
D)Measuring the length of an item.

Accepted Answer

The binomial distribution is used to model the number of successes in a fixed number of independent Bernoulli trials, such as coin tossing, where each trial has two possible outcomes (success or failure).

Question 5

If p = .1 and n = 5,then the corresponding binomial distribution is
A)Right skewed
B)Left skewed
C)Symmetric
D)Bimodal

Accepted Answer

The binomial distribution with a small probability of success (p=0.1) and a small sample size (n=5) is right-skewed. The distribution has a longer tail on the right-hand side because there is a higher chance of getting fewer successes than expected.

Question 6

The number of ways to arrange x successes among n trials is equal to
A) 
B) 
C) 
D)

Accepted Answer

The answer of The number of ways to arrange x...

Question 7

If the number of surface nonconformities on a specific size of a metal piece is the discrete random variable in question,then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 nonconformities is most likely given by the binomial distribution.

Accepted Answer

This example is a description of a hypergeometric distribution.

Question 8

A total of 50 raffle tickets are sold for a contest to win a car.If you purchase one ticket,what are your odds against winning?
A)49 to 1
B)50 to 1
C).05
D).01

Accepted Answer

Probability of losing = 1 − probability of winning = 1 − 1/50 = 49/50.

Question 9

A random variable is said to be discrete if
A)Its outcomes are countable
B)It can assume any real number within a given interval
C)The rules of probability apply
D)It can be represented graphically

Accepted Answer

A random variable is said to be discrete if its outcomes are countable, meaning that they can only take on a finite or countably infinite number of values. Examples of discrete random variables include the number of children in a family, the number of heads in a coin toss, or the number of defects in a production run.

Question 10

In a binomial distribution the random variable X is continuous.

Accepted Answer

In a binomial distribution, the random variable X is discrete, not continuous. It represents the number of successes in a fixed number of independent trials with a constant probability of success.

Question 11

If p = .5 and n = 4,then the corresponding binomial distribution is
A)Right skewed
B)Left skewed
C)Symmetric
D)Bimodal

Accepted Answer

When p = .5 and n = 4, the corresponding binomial distribution is symmetric. This means that the probabilities of getting the same number of successes and failures are equal, and the distribution is centered around the mean (np) at 2.

Question 12

The requirement that the probability of success remains constant from trial to trial is a property of the _________________ distribution.
A)Binomial
B)Uniform
C)Normal
D)Poisson

Accepted Answer

The binomial distribution has the property that the probability of success remains constant from trial to trial. This means that each trial is independent and the probability of success or failure does not change throughout the experiment. This is a fundamental requirement for a binomial distribution.

Question 13

If the number of surface nonconformities on a specific size of metal piece is the discrete random variable in question,then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 defectives is given most likely by ___________________ distribution.
A)Binomial
B)Poisson
C)Hypergeometric
D)Both A and B

Accepted Answer

The Poisson distribution is appropriate for modeling the number of events occurring in a fixed interval of time or space, given the rate of occurrence of the event. In this case, the number of surface nonconformities can be modeled using the Poisson distribution if the defect rate is constant across the entire metal sheet. The binomial distribution would be appropriate if the metal sheet was divided into a fixed number of smaller regions, each with a constant probability of containing a defect. The hypergeometric distribution would be appropriate if the metal sheet was sampled without replacement from a larger population of metal sheets with varying defect rates. Therefore, the most appropriate choice is B.

Question 14

A discrete random variable may assume a countable number of outcome values.

Accepted Answer

A discrete random variable can only take on specific, countable values.

Question 15

The mean of the binomial distribution is equal to: A)p B)np C)p^x (1-p)^n-x D)(n)(p)(1-p) E)

Accepted Answer

The mean of a binomial distribution is given by np, where n is the number of trials and p is the probability of success in each trial.

Question 16

Which of the following is a valid probability value for a discrete random variable?
A).2
B)1.01
C)-.7
D)All of the above

Accepted Answer

A valid probability value for a discrete random variable must be a number between 0 and 1, inclusive. Option A is the only value that satisfies this condition. Option B is greater than 1 and Option C is a negative value which are both invalid probability values. Therefore, the correct choice is A).

Question 17

Which one of the following statements is not an assumption of the binomial distribution?
A)Sampling is with replacement.
B)The experiment consists of n identical trials.
C)The probability of success remains constant from trial to trial.
D)Trials are independent of each other.
E)Each trial results in one of two mutually exclusive outcomes.

Accepted Answer

The answer of Which one of the following statements is...

Question 18

The binomial experiment consists of n independent,identical trials,each of which results in either success or failure and is such that the probability of success on any trial is the same.

Accepted Answer

This is the definition of a binomial experiment.

Question 19

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-thru fast food restaurant is 3 in ten minutes,what is the probability that exactly 4 cars will arrive in a five minute interval?
A)Binomial
B)Poisson
C)Both of the above
D)None of the above

Accepted Answer

The Poisson distribution can be used to solve this problem as it deals with the number of events occurring in a fixed time interval when the events occur independently and at a constant rate. In this case, we have the average rate of arrival (λ) which is 3 cars in ten minutes. Using λ = (5/10) * 3 = 1.5 cars in a 5-minute interval, we can calculate the probability of exactly 4 cars arriving in 5 minutes using the Poisson distribution. The binomial distribution would be used if the problem involved a fixed number of trials with a binary outcome (e.g. success or failure).

Question 20

The variable "home ownership" can take on one of two values,1 if the person living in a home owns the home and zero if the person living in a home does not own the home is an example of a discrete random variable.

Accepted Answer

This statement describes a situation where the variable "home ownership" only takes on two possible values, either 1 or 0. This is a characteristic of a discrete random variable, where the possible outcomes are countable and finite. Therefore, the statement is true and the answer is A.

Quiz 5: Discrete Random Variables

The mean of the binomial distribution is np(1-p).

A Poisson random variable is a continuous variable that can be used to describe the number of occurrences of an event over a specified interval of time or space.

In a binomial experiment,the results of one trial are dependent on the results of other trials.

The binomial distribution is characterized by situations that are analogous to

If p = .1 and n = 5,then the corresponding binomial distribution is

The number of ways to arrange x successes among n trials is equal to

A total of 50 raffle tickets are sold for a contest to win a car.If you purchase one ticket,what are your odds against winning?

A random variable is said to be discrete if

In a binomial distribution the random variable X is continuous.

If p = .5 and n = 4,then the corresponding binomial distribution is

The requirement that the probability of success remains constant from trial to trial is a property of the _________________ distribution.

A discrete random variable may assume a countable number of outcome values.

The mean of the binomial distribution is equal to:

Which of the following is a valid probability value for a discrete random variable?

Which one of the following statements is not an assumption of the binomial distribution?

The binomial experiment consists of n independent,identical trials,each of which results in either success or failure and is such that the probability of success on any trial is the same.

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-thru fast food restaurant is 3 in ten minutes,what is the probability that exactly 4 cars will arrive in a five minute interval?

The variable "home ownership" can take on one of two values,1 if the person living in a home owns the home and zero if the person living in a home does not own the home is an example of a discrete random variable.