Question 1

The only two types of random variables are discrete and continuous random variables.

Accepted Answer

Discrete random variables can take on a countable number of values, while continuous random variables can take on any value within a given range, covering all possible values. These are the two main classifications of random variables in statistics.

Question 2

When a single value is randomly chosen from a discrete distribution, the different possible values are mutually exclusive.

Accepted Answer

In a discrete distribution, each possible value is distinct and separate, meaning the occurrence of one value excludes the possibility of any other value occurring at the same time.

Question 3

If a random variable is discrete, it means that the outcome for the random variable can take on only one of two possible values.

Accepted Answer

A discrete random variable can take on a finite or countably infinite number of values, not limited to just two.

Question 4

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend:  Based on this information, the expected number of injuries per weekend is 2.25.

Accepted Answer

The answer of The Ski Patrol at Criner Mountain Ski...

Question 5

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract:  Based on this information, the profit standard deviation for the company if it takes the contract is < $20,000.

Accepted Answer

The answer of The Argon Construction Company has the opportunity...

Question 6

A random variable is generated when a variable's value is determined by using classical probability.

Accepted Answer

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon, not necessarily determined by classical probability.

Question 7

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract:  Based on this information, the probability of profit being at least $80,000 is 0.85.

Accepted Answer

The answer of The Argon Construction Company has the opportunity...

Question 8

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract:  Based on this information, the expected profit for the company if it takes the contract is $67,000.

Accepted Answer

The answer of The Argon Construction Company has the opportunity...

Question 9

A probability distribution with an expected value greater than the expected value of a second probability distribution will also have a higher standard deviation.

Accepted Answer

The expected value (mean) of a probability distribution does not determine its standard deviation. Two distributions can have different means but the same standard deviation, or a distribution with a higher mean can have a lower standard deviation than another.

Question 10

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend:  Based on this information, the standard deviation for the number of injuries per weekend is 2.25.

Accepted Answer

The answer of The Ski Patrol at Criner Mountain Ski...

Question 11

The time required to assemble two components into a finished part is recorded for each employee at the plant. The resulting random variable is an example of a continuous random variable.

Accepted Answer

The time required to assemble components can take any value within a range, making it a continuous random variable since it can include fractions of seconds or minutes.

Question 12

The number of no-shows for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution:  Based on this information, the most likely number of no-shows on any given day is 0 customers.

Accepted Answer

The answer of The number of no-shows for dinner reservations...

Question 13

The Colbert Real Estate Agency has determined the number of home showings given by its agents is the same each day of the week. Then the variable, number of showings, is a continuous distribution.

Accepted Answer

The number of home showings is a count of occurrences, which makes it a discrete variable, not continuous. Continuous variables can take any value within a range, while discrete variables can only take specific, separate values (like counts).

Question 14

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract:  Based on this information, the probability of profit being < $80,000 is 0.55.

Accepted Answer

The answer of The Argon Construction Company has the opportunity...

Question 15

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract:  Based on this information, the probability that the profit is $80,000 or less is 0.55.

Accepted Answer

The answer of The Argon Construction Company has the opportunity...

Question 16

When a market research manager records the number of potential customers who were surveyed indicating that they like the product design, the random variable, number who like the design, is a discrete random variable.

Accepted Answer

The number of potential customers who like the product design is countable, making it a discrete random variable.

Question 17

The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

Accepted Answer

A graph of a discrete random variable is often represented by a histogram where each bar represents the probability of a possible outcome.

Question 18

The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution:  Based on this information, the standard deviation for the number of no-shows is about 0.36 customers.

Accepted Answer

The answer of The number of no-shows each day for...

Question 19

The random variable, number of customers entering a store between 9 AM and noon, is an example of a discrete random variable.

Accepted Answer

The number of customers is countable and can only take on integer values, making it a discrete random variable.

Question 20

The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution:  Based on this information, the expected number of no-shows is 1.65 customers.

Accepted Answer

The answer of The number of no-shows each day for...

Quiz 5: Discrete Probability Distributions

The only two types of random variables are discrete and continuous random variables.

When a single value is randomly chosen from a discrete distribution, the different possible values are mutually exclusive.

If a random variable is discrete, it means that the outcome for the random variable can take on only one of two possible values.

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Based on this information, the expected number of injuries per weekend is 2.25.

A random variable is generated when a variable's value is determined by using classical probability.

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability of profit being at least $80,000 is 0.85.

A probability distribution with an expected value greater than the expected value of a second probability distribution will also have a higher standard deviation.

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Based on this information, the standard deviation for the number of injuries per weekend is 2.25.

The time required to assemble two components into a finished part is recorded for each employee at the plant. The resulting random variable is an example of a continuous random variable.

The number of no-shows for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: Based on this information, the most likely number of no-shows on any given day is 0 customers.

The Colbert Real Estate Agency has determined the number of home showings given by its agents is the same each day of the week. Then the variable, number of showings, is a continuous distribution.

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability of profit being < $80,000 is 0.55.

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability that the profit is $80,000 or less is 0.55.

When a market research manager records the number of potential customers who were surveyed indicating that they like the product design, the random variable, number who like the design, is a discrete random variable.

The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: Based on this information, the standard deviation for the number of no-shows is about 0.36 customers.

The random variable, number of customers entering a store between 9 AM and noon, is an example of a discrete random variable.

The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: Based on this information, the expected number of no-shows is 1.65 customers.