Question 1

The weight of an object is an example of
A) a continuous random variable.
B) a discrete random variable.
C) either a continuous or a discrete random variable, depending on the nature of the object.
D) either a continuous or a discrete random variable, depending on the unit of measurement.

Accepted Answer

The weight of an object can take on any value within a certain range and thus is a continuous random variable.

Question 2

A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a
A) uniform probability distribution.
B) binomial probability distribution.
C) hypergeometric probability distribution.
D) normal probability distribution.

Accepted Answer

A binomial probability distribution is defined as the probability of x successes in n trials, with a fixed probability of success on each trial. Therefore, this is the appropriate choice for the given scenario. A uniform probability distribution assumes that all outcomes are equally likely, a hypergeometric probability distribution involves sampling without replacement, and a normal probability distribution is used for continuous variables.

Question 3

The Poisson probability distribution is a
A) continuous probability distribution.
B) discrete probability distribution.
C) uniform probability distribution.
D) normal probability distribution.

Accepted Answer

The Poisson probability distribution is a discrete probability distribution that models the number of events occurring in a fixed interval of time or space. It is commonly used in probability and statistics to model rare events.

Question 4

Which of the following is a required condition for a discrete probability function?
A) $\Sigma$f(x) = 0 for all values of x
B) f(x) $\geq$ 1 for all values of x
C) f(x) < 0 for all values of x
D) $\Sigma$f(x) = 1 for all values of x

Accepted Answer

For a discrete probability function, the sum of the probabilities of all possible outcomes must equal 1.

Question 5

The binomial probability distribution is used with
A) a continuous random variable.
B) a discrete random variable.
C) a uniform random variable.
D) an intermittent random variable.

Accepted Answer

The binomial probability distribution is used with a discrete random variable that has only two possible outcomes (success or failure) for each trial. It is commonly used in experiments where each trial is independent and the probability of success remains constant across all trials.

Question 6

A continuous random variable may assume
A) any numerical value in an interval or collection of intervals.
B) finite number of values in a collection of intervals.
C) an infinite sequence of values.
D) only the positive integer values in an interval.

Accepted Answer

A continuous random variable can take on any numerical value within an interval or collection of intervals, meaning it has an infinite number of possible values. This is in contrast to a discrete random variable, which can only take on a finite or countable number of values.

Question 7

A numerical description of the outcome of an experiment is called a
A) descriptive statistic.
B) probability function.
C) variance.
D) random variable.

Accepted Answer

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon. It is a way to assign numbers to outcomes of an experiment, thus providing a numerical description of those outcomes.

Question 8

The expected value of a discrete random variable
A) is the most likely or highest probability value for the random variable.
B) will always be one of the values x can take on, although it may not be the highest probability value for the random variable.
C) is the average value for the random variable over many repeats of the experiment.
D) is the value it is expected to assume in the next trial.

Accepted Answer

The expected value of a discrete random variable is the average value for the random variable over many repeats of the experiment. This means it may not be the most likely or highest probability value, and it is not necessarily the value it is expected to assume in the next trial.

Question 9

The number of customers that enter a store during one day is an example of
A) a continuous random variable.
B) a discrete random variable.
C) either a continuous or a discrete random variable, depending on whether odd or even number of the customers enter.
D) either a continuous or a discrete random variable, depending on the gender of the customers.

Accepted Answer

The number of customers entering a store during one day is a discrete random variable because it can only take on whole number values (e.g. 0 customers, 1 customer, 2 customers, etc.).

Question 10

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment.The random variable in this experiment is a
A) discrete random variable.
B) continuous random variable.
C) mixed type random variable.
D) multivariate random variable.

Accepted Answer

Speed is a continuous variable as it can take on any value within a range. Therefore, the random variable in this experiment is a continuous random variable.

Question 11

A weighted average of the values of a random variable, where the probability function provides weights, is known as
A) the probable value.
B) the median value.
C) the expected value.
D) the variance.

Accepted Answer

The expected value of a random variable is the weighted average of its values, where the probabilities provide the weights. The probable value is the value that has highest probability, and the median is the middle value in a data set when arranged in order of increasing or decreasing values. The variance is a measure of how spread out the values of a random variable are from the expected value.

Question 12

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material.The probability distribution that has the greatest chance of applying to this situation is the
A) Normal distribution.
B) Binomial distribution.
C) Poisson distribution.
D) Uniform distribution.

Accepted Answer

The Poisson distribution is used to model the number of rare events occurring in a fixed amount of time/space. Blemishes or flaws in a 100 feet material can be considered rare events, and hence the Poisson distribution is the most suitable option. The normal distribution assumes a continuous variable and does not fit the discrete nature of the blemish count in a fixed space. The binomial distribution assumes a fixed number of trials, which is not applicable in this case. The uniform distribution assumes equal probability across a range of values, which is not the case for blemishes occurring in a material.

Question 13

Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?
A) The experiment has a sequence of n identical trials
B) Exactly two outcomes are possible on each trial
C) The trials are dependent
D) The probabilities of the outcomes do not change from one trial to another

Accepted Answer

The binomial probability distribution assumes that the trials are independent. If the trials are dependent, then a different distribution may need to be used.

Question 14

Twenty percent of the students in a class of 100 are planning to go to graduate school.The standard deviation of this binomial distribution is
A) 20.
B) 16.
C) 4.
D) 2.

Accepted Answer

The standard deviation of a binomial distribution is given by the formula 
σ = √(npq) 
where n is the sample size, p is the probability of success, and q is the probability of failure (q = 1 - p). 
In this case, n = 100 and p = 0.20, so q = 0.80. 
Substituting these values into the formula, we get 
σ = √(100 x 0.20 x 0.80) 
σ = √(16) 
σ = 4 
Therefore, the standard deviation of this binomial distribution is 4, which corresponds to choice C.

Question 15

Four percent of the customers of a mortgage company default on their payments.A sample of five customers is selected.What is the probability that exactly two customers in the sample will default on their payments?
A) 0.2592
B) 0.0142
C) 0.9588
D) 0.7408

Accepted Answer

This is a binomial probability problem with n=5, p=0.04, and x=2. Using the binomial probability formula: P(x=2) = (5 choose 2)*(0.04)^2*(0.96)^3 = 0.0142 (using a binomial probability calculator). Therefore, the answer is B.

Question 16

A description of the distribution of the values of a random variable and their associated probabilities is called a
A) probability distribution.
B) empirical discrete distribution.
C) bivariate distribution.
D) table of binomial probability.

Accepted Answer

A probability distribution is specifically defined as the description of the distribution of values of a random variable and their associated probabilities. Empirical discrete distribution refers to the distribution of observed data, which may or may not be a probability distribution. Bivariate distribution refers to the distribution of two random variables, not just one. A table of binomial probability is a specific type of probability distribution for a specific type of random variable (binomial).

Question 17

Which of the following is a required condition for a discrete probability function?
A) f(x) $\leq$ 0 for all values of x
B) $\Sigma$f(x) = 1 for all values of x
C) $\Sigma$f(x) = 0 for all values of x
D) $\Sigma$f(x) $\geq$ 1 for all values of x

Accepted Answer

A discrete probability function must sum to 1 over all possible values of x.

Question 18

Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?
A) The experiment has at least two possible outcomes
B) Exactly two outcomes are possible on each trial
C) The trials are dependent on each other
D) The probabilities of the outcomes changes from one trial

Accepted Answer

The binomial probability distribution is applicable to experiments where there are a fixed number of trials, exactly two possible outcomes (often denoted as success or failure) on each trial, the trials are independent of each other, and the probability of success remains constant across all trials. Therefore, option B is the only one that satisfies this condition.

Question 19

A measure of the average value of a random variable is called a(n)
A) variance.
B) standard deviation.
C) expected value.
D) coefficient of variation.

Accepted Answer

The expected value is a measure of the average value of a random variable. The variance and standard deviation are measures of the variability or spread of a random variable, while the coefficient of variation is a measure of the relative variability or spread of a random variable.

Question 20

The expected value of a random variable is
A) the value of the random variable that should be observed on the next repeat of the experiment
B) the value of the random variable that occurs most frequently
C) the square root of the variance
D) None of these alternatives is correct.

Accepted Answer

The expected value of a random variable is a theoretical mean of all possible outcomes, weighted by their probabilities, not necessarily any of the described options.

Quiz 5: Discrete Probability Distributions

The weight of an object is an example of

A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a

The Poisson probability distribution is a

Which of the following is a required condition for a discrete probability function?

The binomial probability distribution is used with

A continuous random variable may assume

A numerical description of the outcome of an experiment is called a

The expected value of a discrete random variable

The number of customers that enter a store during one day is an example of

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment.The random variable in this experiment is a

A weighted average of the values of a random variable, where the probability function provides weights, is known as

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material.The probability distribution that has the greatest chance of applying to this situation is the

Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?

Twenty percent of the students in a class of 100 are planning to go to graduate school.The standard deviation of this binomial distribution is

Four percent of the customers of a mortgage company default on their payments.A sample of five customers is selected.What is the probability that exactly two customers in the sample will default on their payments?

A description of the distribution of the values of a random variable and their associated probabilities is called a

Which of the following is a required condition for a discrete probability function?

Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?

A measure of the average value of a random variable is called a(n)

The expected value of a random variable is