Question 1

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)$\ge$ 1 for all values of x
C)f(x)< 0 for all values of x
D) $\Sigma$(x)= 1 for all values of x

Accepted Answer

A discrete probability function must sum up to 1 for all possible values of x. This ensures that the total probability of all possible outcomes is equal to 1, which is a fundamental property of probability. Choices A, B, and C do not meet this requirement.

Question 2

A random variable that can assume only a finite number of values is referred to as a(n)
A)infinite sequence
B)finite sequence
C)discrete random variable
D)discrete probability function

Accepted Answer

A discrete random variable is defined as one whose set of possible values is finite or countably infinite, meaning it can be listed in order or counted. Therefore, option C is the correct choice.

Question 3

The number of electrical outages in a city varies from day to day.Assume that the number of electrical outages (x)in the city has the following probability distribution.

The mean and the standard deviation for the number of electrical outages (respectively)are
A)2.6 and 5.77
B)0.26 and 0.577
C)3 and 0.01
D)0 and 0.8

Accepted Answer

B

Question 4

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)complex random variable
D)simplex random variable

Accepted Answer

The speed of automobiles on a highway is a continuous variable as it can take on any value within a certain range (e.g. 0-100 mph), and not just specific, distinct values. Therefore, the random variable in this experiment is a continuous random variable.

Question 5

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 the average value of a random variable, while variance and standard deviation measure the spread of the data around the expected value. Coefficient of variation is a measure of relative variability, which is the standard deviation divided by the expected value. Therefore, the best choice is C, expected value, as it directly corresponds to the definition given in the question.

Question 6

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 weight of the object
D)either a continuous or a discrete random variable depending on the units of measurement

Accepted Answer

The weight of an object can take on any value within a certain range, for example, a person's weight could be anywhere between 50kg and 100kg. Therefore, weight is a continuous random variable since it can take on any value within a continuous range.

Question 7

Which of the following is not a required condition for a discrete probability function?
A)f(x) $\ge$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)$\ge$1 for all values of x

Accepted Answer

A discrete probability function must sum to 1, not 0, across all possible values of x.

Question 8

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 answer of Twenty percent of the students in a...

Question 9

A continuous random variable may assume
A)any value in an interval or collection of intervals
B)only integer values in an interval or collection of intervals
C)only fractional values in an interval or collection of intervals
D)only the positive integer values in an interval

Accepted Answer

A continuous random variable can take on any value within a range or interval of values. This is because the probability of any specific value occurring is zero for a continuous random variable.

Question 10

When sampling without replacement,the probability of obtaining a certain sample is best given by a
A)hypergeometric distribution
B)binomial distribution
C)Poisson distribution
D)normal distribution

Accepted Answer

The hypergeometric distribution is the best choice for sampling without replacement, as it takes into account the changing population size as each item is selected. The binomial distribution assumes independent trials with replacement, which is not the case in sampling without replacement. The Poisson and normal distributions are not appropriate for sampling without replacement.

Question 11

The variance is a measure of dispersion or variability of a random variable.It is a weighted average of the
A)square root of the deviations from the mean
B)square root of the deviations from the median
C)squared deviations from the median
D)squared deviations from the mean

Accepted Answer

The variance is calculated by taking the squared deviations from the mean and weighting them by their probabilities. Therefore, option D is the correct choice as it calculates the variance using squared deviations from the mean.

Question 12

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 distribution problem with n=5, p=0.04, and x=2. The formula for the probability of exactly x successes in n trials is:

P(x) = (n C x) * p^x * (1-p)^(n-x)

Where (n C x) represents combinations or ways to choose x items from a set of n items.

Plugging in the values, we get:

P(2) = (5 C 2) * 0.04^2 * (1-0.04)^(5-2) 
      = 10 * 0.0016 * 0.941192 
      = 0.0142

Therefore, the probability that exactly two customers in the sample will default on their payments is 0.0142.

Question 13

A description of the distribution of the values of a random variable and their associated probabilities is called a
A)probability distribution
B)random variance
C)random variable
D)expected value

Accepted Answer

A probability distribution is specifically defined as a description of the distribution of values of a random variable and their associated probabilities. Options B, C, and D are not accurate descriptions of a probability distribution.

Question 14

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy.The random variable in this experiment is a
A)discrete random variable
B)continuous random variable
C)complex random variable
D)simplex random variable

Accepted Answer

The random variable in this experiment is the number of insurance policies sold, which can only take on discrete values (i.e. 0, 1, 2, 3, etc.). Therefore, it is a discrete random variable.

Question 15

Variance is
A)a measure of the average,or central value of a random variable
B)a measure of the dispersion of a random variable
C)the square root of the standard deviation
D)the sum of the squared deviation of data elements from the mean

Accepted Answer

The answer of Variance is
A)a measure of the average,or central...

Question 16

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 17

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

Accepted Answer

The weighted average of a random variable with the given probability function as weights is known as the expected value. Therefore, the correct answer is C. A probability function is a mathematical function that gives the probability of occurrence of specific events, and a random variable is a variable whose values depend on the outcomes of a random event. A random function is not a relevant concept in mathematics.

Question 18

The standard deviation is the
A)variance squared
B)square root of the sum of the deviations from the mean
C)same as the expected value
D)positive square root of the variance

Accepted Answer

The standard deviation is defined as the positive square root of the variance.

Question 19

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 the number of the customers
D)either a continuous or a discrete random variable,depending on the gender of the customers

Accepted Answer

The number of customers that enter a store during one day is a discrete random variable because it can only take on specific, whole number values (i.e. the number of customers cannot be 1.5 or 2.75, it can only be 1, 2, 3, etc.).

Question 20

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

The scenario described fits the definition of a binomial probability distribution, where the probability of success remains constant throughout each of the n trials. The other options either have changing probabilities or different conditions for the trials.

Quiz 5: Discrete Probability Distributions

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

A random variable that can assume only a finite number of values is referred to as a(n)

The number of electrical outages in a city varies from day to day.Assume that the number of electrical outages (x) in the city has the following probability distribution. The mean and the standard deviation for the number of electrical outages (respectively) are

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

The weight of an object is an example of

Which of the following is not a required condition for a discrete probability function?

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 continuous random variable may assume

When sampling without replacement,the probability of obtaining a certain sample is best given by a

The variance is a measure of dispersion or variability of a random variable.It is a weighted average of the

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

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy.The random variable in this experiment is a

Variance is

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

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

The standard deviation is the

The number of customers that enter a store during one day 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