Question 1

A characteristic of a Bernoulli process is that the probability of success remains the same from one trial to the next.

Accepted Answer

This is one of the defining characteristics of a Bernoulli process - the probability of success (or failure) remains constant from one trial to the next.

Question 2

Approximately 84% of persons age 70 to 84 live in their own household and are income-qualified for home purchases.If four persons are randomly selected from this population,the probability that exactly two of the four live in their own household and are income-qualified is:
A) 0.8916
B) 0.4182
C) 0.0138
D) 0.5404
E) 0.1084

Accepted Answer

The probability can be calculated using the binomial probability formula: P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n=4, k=2, and p=0.84. This results in approximately 0.1084.

Question 3

A characteristic of a Bernoulli process is that the trials are statistically dependent; that is,the outcome in any trial is affected by the outcomes of earlier trials,and it does affect the outcomes of later trials.

Accepted Answer

A Bernoulli process is characterized by trials that are statistically independent, meaning the outcome of any given trial does not affect, nor is it affected by, the outcomes of any other trials.

Question 4

The number of life insurance policy holders is an example of a discrete random variable.

Accepted Answer

A discrete random variable is a variable that can only take on specific, isolated values. The number of life insurance policy holders is a discrete variable because it can only take on whole number values (i.e. 0 policy holders, 1 policy holder, 2 policy holders, etc.).

Question 5

Theoretically,the number of times an event can occur over the given time span in a Poisson distribution has no limit.

Accepted Answer

In a Poisson distribution, the number of events that can occur in a given time span can technically be infinite, although the probability of extremely high numbers of events becomes increasingly small.

Question 6

One characteristic of a discrete probability distribution is that values of x are exhaustive.

Accepted Answer

In a discrete probability distribution, the possible values of x are defined and limited, meaning they are exhaustive.

Question 7

A table,formula,or graph that shows all possible values a random variable can assume,together with their associated probabilities is referred to as:
A) Discrete probability distribution
B) Continuous probability distribution
C) Mixed probability distribution
D) Contaminated probability distribution

Accepted Answer

A discrete probability distribution is a table, formula, or graph that shows all possible values a random variable can assume, together with their associated probabilities. It applies to situations where the random variable can only take on certain values (discrete values) and each of those values has a specific probability of occurring.

Question 8

For a Bernoulli process in which the number of trials is large and the probability of success on any given trial is very small,the Poisson distribution can be used as an approximation to the binomial distribution.

Accepted Answer

This is true. When n (the number of trials) is large and p (the probability of success on any given trial) is small, the binomial distribution can become unwieldy and computationally intensive. In such cases, the Poisson distribution can be used as an approximation of the binomial distribution. This is known as the Poisson approximation to the binomial distribution.

Question 9

The number of hungry people in Ethiopia is an example of a discrete random variable.

Accepted Answer

A discrete random variable is a variable that can take on a finite or countably infinite number of distinct values. In this case, the number of hungry people in Ethiopia can only take on integer values (e.g. 0, 1, 2, 3, ...) which makes it a discrete random variable.

Question 10

The binomial distribution is best used to describe the number of customers arriving at a service point during a given period of time.

Accepted Answer

The Poisson distribution is best used for describing the number of customers arriving at a service point during a given period of time, as it deals with the occurrence of events in a fixed interval of time or space. The binomial distribution is used for scenarios with a fixed number of trials and only two possible outcomes (success or failure) in each trial.

Question 11

The probability of success in a hypergeometric distribution does not remain constant from one trial to another.

Accepted Answer

In a hypergeometric distribution, the probability of success depends on the number of successes and failures in the population, as well as the size of the sample. As each trial of the hypergeometric distribution involves a different sample size and/or different numbers of successes and failures, the probability of success will not remain constant from one trial to another.

Question 12

The binomial distribution requires that the probability of a success for each trial remains constant.

Accepted Answer

The binomial distribution assumes that the probability of success remains constant for each trial. This means that the probability of success does not change from one trial to another.

Question 13

Which of the following is not a characteristic of a discrete probability distribution?
A) The sum of the probabilities is one.
B) The values of x are exhaustive.
C) The value for the probability of any given x ranges from 0 to 1.
D) The values of x are mutually exclusive.
E) The sum of the probabilities for all possible values of x must be between 0 and 1.

Accepted Answer

The sum of the probabilities for all possible values of x in a discrete probability distribution must equal exactly 1, not between 0 and 1. This ensures that the distribution accounts for all possible outcomes.

Question 14

A new car salesperson knows that he sells cars to one customer out of 20 who enter the showroom.The probability that he will sell a car to exactly two of the next three customers is:
A) 0.9939
B) 0.0075
C) 0.0071
D) 0.0851
E) 0.1354

Accepted Answer

The probability of selling a car to one customer out of twenty is 1/20 = 0.05.
The probability of not selling a car to one customer out of twenty is 19/20 = 0.95.
Using the binomial distribution, the probability of selling a car to exactly two of the next three customers is:

P(2) = (3 choose 2)*(0.05)^2*(0.95)^1 = 3*0.0025*0.95 = 0.0071

Therefore, the answer is C.

Question 15

The driving time between Big Rapids and Grand Rapids is an example of a discrete random variable.

Accepted Answer

The driving time between Big Rapids and Grand Rapids is a continuous random variable.

Question 16

One characteristic of a discrete probability distribution is that the sum of the probabilities for all the possible values for x must be between 0 and 1.

Accepted Answer

The sum of the probabilities for all possible values of x in a discrete probability distribution must equal 1, not be between 0 and 1.

Question 17

The hypergeometric distribution is similar to the binomial distribution in that successive trials are considered to be independent of one another.

Accepted Answer

The hypergeometric distribution does not assume independence between trials, as it involves selecting items without replacement. The binomial distribution, on the other hand, assumes independence between trials with replacement.

Question 18

Which of the following most likely represents a discrete random variable?
A) Length of time between calls to an 800 number.
B) The number of years completed in the military services.
C) The S & P Industrial average of stock prices.
D) The amount of retail sales on a given day.
E) Length of time for which an apartment in a large complex remains vacant.

Accepted Answer

A discrete random variable is one that can take on a countable number of values. The length of time between calls to an 800 number (A) and the S & P Industrial average of stock prices (C) are continuous variables, meaning they can take on any value within a given range. The amount of retail sales on a given day (D) and the length of time for which an apartment in a large complex remains vacant (E) also have a continuous range of values. The number of years completed in the military services (B), on the other hand, can only take on discrete integer values (e.g. 1 year, 2 years, 3 years, etc.), making it the most likely choice for a discrete random variable.

Question 19

Which of the following is a discrete random variable?
A) The average daily consumption of water in a U.S.household.
B) The weight of football players in the NFL.
C) The number of three-point shots completed in a college basketball game.
D) The time required to drive from Dallas to Denver.
E) The average daily temperature in the world.

Accepted Answer

A discrete random variable is one that can only take on specific values, such as integers. The number of three-point shots completed in a college basketball game fits this definition, as it can only be a whole number. The other options are not discrete random variables as they can take on a continuous range of values.

Question 20

Theoretically,the number of successes in a binomial distribution has no limit.

Accepted Answer

In a binomial distribution, the number of successes is limited by the number of trials, since it represents the number of successes in a fixed number of independent Bernoulli trials.

Quiz 6: Discrete Probability Distributions