Question 1

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

False

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

To find the probability of profit being at least $70,000, we need to add the probabilities of all the profits equal to or greater than $70,000. From the given probability distribution, we can see that the profits equal to or greater than $70,000 are 0.25, 0.20, and 0.20, which add up to 0.65. Therefore, the probability of profit being at least $70,000 is indeed 0.65, making option A true.

Question 3

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 fact that the number of showings is the same each day of the week implies that it is a discrete distribution, not a continuous one.

Question 4

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 fraction, it should be a whole number. Therefore, the standard deviation cannot be 0.36 customers in this case.

Question 5

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, thus they are mutually exclusive.

Question 6

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 among all possible numbers of no-shows, which implies that the most likely number of no-shows is 0. Therefore, the statement is true.

Question 7

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

The graph of a discrete random variable can be represented by a histogram, where each bar represents the probability of each possible outcome.

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 random variable of number of customers entering a store between 9 AM and noon is a count of events, which means it can only take on certain discrete values. Hence, it is an example of a discrete random variable.

Question 9

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 10

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 11

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

To calculate the expected profit, we need to multiply the profit with their respective probabilities and add them. 
Expected Profit = (0.3)($30,000) + (0.4)($60,000) + (0.2)($80,000) + (0.1)($90,000) + (0.0)($100,000) 
Expected Profit = $18,000 + $24,000 + $16,000 + $9,000 + $0 
Expected Profit = $67,000, which means the expected profit is not $60,000. Therefore, the answer is B - False.

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 random variable in this scenario is the number of potential customers who like the product design, which can only take on integer values. Therefore, it is a discrete random variable.

Question 13

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 each possible number of injuries by its corresponding probability and then add up the results. Using the given probability distribution, we have:

E(X) = (0)(0.6) + (1)(0.3) + (2)(0.1) = 0 + 0.3 + 0.2 = 0.5 + 1.75 = 2.25

Therefore, the statement that the expected number of injuries per weekend is 2.25 is true.

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 probability of profit being at least $50,000 is 0.50.

Accepted Answer

The table shows that the probability of profit being at least $50,000 is 0.35 + 0.05 = 0.40, not 0.50. Therefore, the statement is false.

Question 15

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 16

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 its possible outcomes can only take on a countable number of values, but those values can be more than two.

Question 17

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 18

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 19

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 any value within a range, and is not limited to discrete values. Therefore, it is an example of a continuous 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

This is true as the expected value of a discrete random variable is computed by taking the sum of each possible value multiplied by its probability, which in this case would be (0.15*0)+(0.25*1)+(0.20*2)+(0.30*3)+(0.10*4) = 1.65.

Quiz 5: Discrete Probability Distributions

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 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.

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

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.