Question 1

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 that considers the probability function as weights is known as the expected value. It represents the average outcome that we can expect in the long run when we repeat the experiment several times.

Question 2

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. Therefore, option D is the correct answer. Option A is incorrect because the variance is the square of the standard deviation, not the other way around. Option B is incorrect because it describes the calculation of the variance, not the standard deviation. Option C is incorrect because the expected value is a completely different concept in statistics.

Question 3

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 specifically designed for situations where sampling is done without replacement. It is meant to represent situations where the probability of success changes with each draw, which is not the case for the binomial distribution. The Poisson distribution is used to model rare events, and the normal distribution assumes sampling is done with replacement and the sample size is large.

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 can take on any value within a certain range, making it a continuous random variable.

Question 5

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 is a continuous random variable because it can take on any value within a certain range (e.g. a weight can be 5.7 pounds or 5.7001 pounds). It is not a discrete random variable because there are an infinite number of possible values between any two given weights.

Question 6

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 defines how probabilities are distributed across the values of a random variable, making A the correct choice. B and D are not accurate descriptions of a distribution, and C is just a type of variable that can take on different values with different probabilities.

Question 7

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 $\sqrt{np(1-p)}$, where $n$ is the number of trials and $p$ is the probability of success in each trial. In this case, $n=100$ and $p=0.2$, so the standard deviation is $\sqrt{100\cdot 0.2\cdot 0.8} = 4$. Therefore, the best choice is $\boxed{	ext{(C) }4}$.

Question 8

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

Variance is a measure of how spread out a data set is. It is calculated by taking the difference between each data point and the mean, squaring those differences, adding them up, and then dividing by the number of data points. Variance is usually represented by the symbol σ².

Question 9

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)≥ 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

The required condition for a discrete probability function is that the sum of all its probabilities (represented by f(x)) must be equal to 1 for all values of x. Therefore, the correct choice is D.

Question 10

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 measure of the average value of a random variable is called its expected value. This is different from the variance and standard deviation, which measure the spread and deviation of the values from the expected value. The coefficient of variation is a measure of the variability of a random variable relative to its mean and is calculated as the ratio of the standard deviation to the mean.

Question 11

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 definition given matches the characteristics of a binomial probability distribution, which is used to model situations with a fixed number of trials and a binary outcome (success or failure) with a constant probability of success.

Question 12

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 one that can only take on a finite or countably infinite number of values, so option C is the best choice. Options A and B refer to sequences, but do not specify if they are infinite or finite, so they cannot be correct. Option D refers to a function that assigns probabilities to each possible value of a discrete random variable, but does not specify that the variable itself is finite, so it is not the best choice.

Question 13

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

Accepted Answer

The answer of Which of the following is not a...

Question 14

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

The answer of The number of electrical outages in a...

Question 15

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 16

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 particular whole number values, such as 0 customers, 1 customer, 2 customers, etc. It cannot take on fractional values like a continuous random variable would. The answer is not C or D because the nature of the variable does not depend on the specific values, such as gender or number of customers.

Question 17

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 of each data point from the mean, weighting them by their probabilities, and taking the average. Therefore, the correct choice is squared deviations from the mean (choice D).

Question 18

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 represents the number of insurance policies sold, which can only take on a finite number of values (0, 1, 2, ..., 80), making it a discrete random variable.

Question 19

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 we are interested in finding P(X=2). Using the binomial probability formula P(X=k) = (n choose k) * p^k * (1-p)^(n-k), we get P(X=2) = (5 choose 2) * 0.04^2 * 0.96^3 = 0.0142. Therefore, the answer is B.

Question 20

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 any value within a specific range or interval. It can take fractional or decimal values, unlike discrete random variables which can only take on specific integer values.

Quiz 5: Discrete Probability Distributions

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

The standard deviation is the

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

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

The weight of an object is an example of

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

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

Variance is

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

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

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

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

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 numerical description of the outcome of an experiment is called a

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

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

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

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 continuous random variable may assume