Question 1

To construct a binomial probability distribution,the number of trials and the probability of success must be known.

Accepted Answer

This statement is correct. Both the number of trials and the probability of success are necessary to construct a binomial probability distribution.

Question 2

A probability distribution is a mutually exclusive and collectively exhaustive listing of experimental outcomes that can occur by chance and their corresponding probabilities.

Accepted Answer

This statement accurately describes what a probability distribution is.

Question 3

A random variable may be either discrete or continuous.

Accepted Answer

This statement is true. A random variable can either take on a finite or countably infinite set of values (discrete) or can take on any value in a continuous range (continuous).

Question 4

A Poisson distribution is a discrete probability distribution.It has the same four characteristics as the binomial,but in addition,the probability of a success is small and the number of trials is relatively large.

Accepted Answer

A Poisson distribution is a discrete probability distribution with the same characteristics as the binomial, but it is used when the probability of success is small and the number of trials is large.

Question 5

A discrete variable may assume fractional or decimal values,but they must have distance between them.

Accepted Answer

The answer of A discrete variable may assume fractional or...

Question 6

A random variable is assigned nominal or numerical values based on the outcomes of an experiment.

Accepted Answer

A random variable can be assigned either nominal or numerical values based on the outcomes of an experiment.

Question 7

A random variable represents the outcomes of an experiment.

Accepted Answer

A random variable is a numerical or categorical value that represents the possible outcomes of an experiment.

Question 8

The Poisson probability distribution is a continuous probability distribution.

Accepted Answer

The Poisson probability distribution is actually a discrete probability distribution, as it deals with the probabilities of counting events that occur in a fixed interval of time or space.

Question 9

If we toss two coins and count the number of heads,there could be 0,1 or 2 heads.The number of heads resulting from this experiment is a random variable.

Accepted Answer

This statement is true. The number of heads resulting from the experiment of tossing two coins is not known with certainty and can take different values, hence it is a random variable.

Question 10

The Poisson probability distribution is always negatively skewed.

Accepted Answer

The Poisson distribution is typically positively skewed, especially when the mean is small. As the mean increases, the distribution becomes more symmetric.

Question 11

The random variable for a Poisson probability distribution can assume an infinite number of values.

Accepted Answer

A Poisson distribution can include any non-negative integer as a possible value, meaning an infinite number of possible values.

Question 12

If Unique Buying Services has 100 employees,there might be 0,or 1,or 2,or 3,or up to 100 employees absent on Monday.In this case,the day of the week is the random variable.

Accepted Answer

The random variable in this context is the number of employees absent, not the day of the week.

Question 13

The probability of a particular outcome must always be between 0 and 100 inclusive.

Accepted Answer

The answer of The probability of a particular outcome must...

Question 14

For a binomial distribution,outcomes of an experiment are classified into one of two mutually exclusive categories (a success or a failure).

Accepted Answer

That is correct, for a binomial distribution, there are only two possible outcomes and they are mutually exclusive (meaning they cannot occur at the same time).

Question 15

For a binomial distribution,each trial has a known number of successes.For example,a four question multiple-choice test can only have zero,one,two,three and four successes (number correct).

Accepted Answer

This statement is true. In a binomial distribution, there are a fixed number of trials and each trial can only have two outcomes (success or failure). The number of successes in each trial is known and fixed, and the total number of possible successes is often limited, as in the example of a multiple-choice test with a set number of questions.

Question 16

A binomial distribution has a characteristic that the trials are independent,which means that the outcome of one trial does not affect the outcome of any other trial.

Accepted Answer

This is a fundamental characteristic of a binomial distribution. Each trial is independent of the others, meaning that the outcome of one trial has no effect on the outcome of any other trial.

Question 17

A discrete random variable can have only certain clearly separated values.

Accepted Answer

Discrete random variables can only take on specific, separate values (such as the number of students in a classroom or the number of heads obtained when flipping a coin), rather than continuous values (such as temperature or height).

Question 18

If we measure the weight of a car,the variable is a discrete random variable.

Accepted Answer

Weight is a continuous random variable as it can take on any value within a certain range, not just isolated values.

Question 19

For a binomial distribution,the probability of a success stays the same for each trial,but the probability of a failure varies from trial to trial.

Accepted Answer

In a binomial distribution, both the probability of success and the probability of failure remain constant across all trials.

Question 20

For a binomial distribution,the data collected are the result of counts.

Accepted Answer

The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, where each trial has two possible outcomes (success or failure). Therefore, the data collected would be in the form of counts of the number of successes in those trials.

Quiz 6: Discrete Probability Distributions