Question 1

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 probability of 0 no-shows is the highest (0.4), which means that it is the most likely number of no-shows on any given day. Therefore, the statement is true.

Question 2

The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road.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 $70,000 is 0.65.

Accepted Answer

True

Question 3

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 4

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 two components can take on a range of values and is not limited to only specific values, making it a continuous random variable.

Question 5

The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road.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 $11,235.

Accepted Answer

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

Question 6

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

If a random variable is discrete, it means that the outcome can take on a countable number of values (e.g. 1, 2, 3, 4...). It does not necessarily mean that there are only two possible values.

Question 7

The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road.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 $60,000.

Accepted Answer

The expected profit can be calculated by multiplying each profit outcome by its corresponding probability and adding up the results. In this case, (0.2 x $40,000) + (0.3 x $60,000) + (0.5 x $80,000) = $20,000 + $18,000 + $40,000 = $78,000. Therefore, the expected profit is $78,000, not $60,000.

Question 8

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 entering the store can only take on integer values and cannot be fraction or continuous, which makes it a discrete random variable.

Question 9

When a single die is rolled,each of the six sides are equally likely.This is an example of a uniform distribution.

Accepted Answer

A uniform distribution means that each outcome is equally likely, which is true for a single die roll with six sides.

Question 10

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

Accepted Answer

When an item is chosen from a discrete distribution, only one value can be selected at a time, making the different possible values mutually exclusive.

Question 11

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 expected value of a discrete random variable is equal to the sum of each possible value multiplied by its probability. Using the given probability distribution, we can calculate the expected value as follows:

(0)(0.4) + (1)(0.35) + (2)(0.15) + (3)(0.1) = 1.65

Therefore, the statement is true.

Question 12

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 statement accurately describes a discrete random variable.

Question 13

The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road.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 $50,000 is 0.50.

Accepted Answer

According to the table, the probability of profit being at least $50,000 is 0.20.

Question 14

The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road.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 $70,500.

Accepted Answer

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

Question 15

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 standard deviation cannot be a decimal value for a discrete random variable. It should be a whole number. Therefore, the statement is false.

Question 16

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

Accepted Answer

The answer of A random variable is generated when a...

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

This statement is correct. A graph of a discrete random variable can be represented by a histogram where the height of each bar corresponds to the probability of each possible outcome.

Question 18

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

To find the expected number of injuries, we multiply the number of injuries possible (0, 1, 2, 3) by their respective probabilities and add them together.

E(X) = (0)(0.10) + (1)(0.35) + (2)(0.45) + (3)(0.10) = 2.25

Therefore, the expected number of injuries per weekend is indeed 2.25.

Question 19

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

If the number of showings is the same each day of the week, it is more likely to be a discrete distribution rather than a continuous one. In a continuous distribution, values can take on any value within a certain range, while in a discrete distribution, values can only take on specific, distinct values.

Question 20

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.

Quiz 5: Discrete Probability Distributions

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.