Question 1

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

Accepted Answer

The expected value of a random variable is the weighted average of its values, where the probabilities serve as weights. Therefore, the correct option is C. Option A, probable value, refers to a value that has the highest probability of occurring. Option B, median value, is the point where half of the values lie above and half lie below, and it may or may not coincide with the expected value. Option D, variance, measures the variability or spread of a random variable, and it is not a weighted average.

Question 2

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 _____ distribution

Accepted Answer

The Poisson distribution is commonly used to model count data, such as the number of blemishes or flaws occurring in a fixed length of textile material. The other options are less appropriate as the normal distribution assumes continuous data, the binomial distribution assumes a fixed number of trials with a binary outcome, and the uniform distribution assumes equal probability for all possible outcomes.

Question 3

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

Accepted Answer

The binomial probability distribution assumes that the trials are independent. Therefore, option C, where the trials are dependent, is not a characteristic of an experiment where the binomial probability distribution is applicable.

Question 4

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

Accepted Answer

A probability distribution is a description of the distribution of values of a random variable along with their associated probabilities. Options B, C, and D do not accurately describe this concept.

Question 5

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

Accepted Answer

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

Question 6

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

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 7

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

Accepted Answer

A discrete probability function must satisfy the condition that the sum of all possible probabilities (represented by f(x)) is equal to 1. Therefore, option D is the correct answer as it satisfies this condition. Option A is incorrect as the sum of probabilities cannot be equal to 0. Option B is incorrect as probabilities cannot be greater than 1. Option C is incorrect as probabilities cannot be negative.

Question 8

A continuous random variable may assume

Accepted Answer

A continuous random variable can take on any numerical value within a given interval or collection of intervals. This is because the probability of a specific value is always zero for a continuous random variable, so it can take on an infinite number of possible values within a given range.

Question 9

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

Accepted Answer

The sum of all probabilities for all events in a discrete probability function must equal 1, which is the definition of a probability distribution. Option A is incorrect because f(x) can be 0 for certain values of x. Option C is incorrect because the sum cannot be 0 unless all probabilities are 0, which is not a valid probability distribution. Option D is incorrect because it implies that the sum of probabilities can be greater than 1, which is not allowed.

Question 10

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

Accepted Answer

The number of customers that enter a store during one day is a countable quantity and can only take on whole-number values, making it a discrete random variable.

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

Accepted Answer

The described probability distribution meets the requirements for a binomial probability distribution, where there are only two possible outcomes (success or failure), each trial is independent, the probability of success remains constant for each trial, and there is a fixed number of trials (n). The binomial distribution is commonly used in experiments and studies where the outcome can be classified into two categories, such as flipping a coin or measuring the success rate of a drug treatment.

Question 12

The weight of an object is an example of

Accepted Answer

The weight of an object can take on any value within a certain range (for example, a weight could be 1.23456 pounds or 2.4567 pounds or any value in between), making it a continuous random variable.

Question 13

The binomial probability distribution is used with a(n) _____ random variable.

Accepted Answer

The binomial probability distribution is used with a discrete random variable, which has a finite number of possible outcomes. It is used to calculate the probability of a certain number of successes in a given number of independent trials with a fixed probability of success.

Question 14

Twenty percent of the students in a class of 400 are planning to go to graduate school. The standard deviation of this binomial distribution is

Accepted Answer

The standard deviation of a binomial distribution is given by the formula sqrt(np(1-p)), where n = sample size, p = probability of success for each trial. Here, n = 400 and p = 0.2 (since 20% of the students are planning to go to graduate school).

Plugging in the values, we get: 
sqrt(400*0.2*0.8) = sqrt(64) = 8

Therefore, the standard deviation of this binomial distribution is 8, which corresponds to choice (C).

Question 15

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

Accepted Answer

The binomial probability distribution is applicable when there are a fixed number of trials, each trial has only two possible outcomes (often called success and failure), the trials are independent, and the probability of success remains constant throughout all trials. Therefore, option B which states that exactly two outcomes are possible on each trial is correct.

Question 16

The expected value of a random variable is

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.

Question 17

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 _____ random variable.

Accepted Answer

The speed of automobiles on a highway can take on any value on a continuous scale (e.g. 55.6 mph, 62.3 mph, etc.), indicating that the random variable is continuous.

Question 18

Three 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?

Accepted Answer

This is a binomial probability problem where n = 5 (number of trials), k = 2 (number of successes), p = 0.03 (probability of success), and q = 1 - p = 0.97 (probability of failure). The formula for binomial probability is P(X = k) = (n choose k) * p^k * q^(n-k). Plugging in the values: P(X = 2) = (5 choose 2) * (0.03)^2 * (0.97)^3 = 10 * 0.0009 * 0.912673 = 0.0082.

Question 19

The Poisson probability distribution is a _____ probability distribution.

Accepted Answer

The Poisson probability distribution is a discrete probability distribution. It is used to model the count of a rare event that occurs randomly over time or space. The probability of observing each count is calculated by a specific formula, making it a discrete probability distribution.

Question 20

The expected value of a discrete random variable

Accepted Answer

The expected value of a discrete random variable is the average value for the random variable over many repeats of the experiment. It is calculated by weighting each possible outcome by its probability and summing them up. This value may not be the most likely or highest probability value for the random variable. It is also not necessarily the value that will occur in the next trial.

Quiz 5: Discrete Probability Distributions

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

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 _____ distribution

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

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

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

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

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

A continuous random variable may assume

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

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

The weight of an object is an example of

The binomial probability distribution is used with a(n) _____ random variable.

Twenty percent of the students in a class of 400 are planning to go to graduate school. The standard deviation of this binomial distribution is

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

The expected value of a random variable is

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 _____ random variable.

Three 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?

The Poisson probability distribution is a _____ probability distribution.

The expected value of a discrete random variable