Question 1

​A probability tree is a graphical representation of how events occur through time, which is useful for calculating probabilities.

Accepted Answer

This statement is true, as a probability tree is a tool used to visualize the possible outcomes of a sequence of events and calculate the probabilities of those outcomes.

Question 2

Find the probability that three or fewer customers are in line.

Accepted Answer

The answer of Find the probability that three or fewer...

Question 3

If it costs $200,000 to drill each well and a successful well will produce $1,000,000 worth of oil over its lifetime, what is the expected net value of this three-well program if no wells are successful?

Accepted Answer

The answer of If it costs $200,000 to drill each...

Question 4

The time students spend in a computer lab during one day is an example of a continuous random variable.

Accepted Answer

Time is a continuous variable as it can take on any value within a range, and the length of time spent in a computer lab can also take on any value within a range. Therefore, it is an example of a continuous random variable.

Question 5

If it costs $200,000 to drill each well and a successful well will produce $1,000,000 worth of oil over its lifetime, what is the expected net value of this three-well program if all three wells are successful?

Accepted Answer

The answer of If it costs $200,000 to drill each...

Question 6

There are two types of random variables, they are:
A) discrete and continuous
B) exhaustive and mutually exclusive
C) complementary and cumulative
D) real and unreal

Accepted Answer

The two types of random variables are discrete and continuous.

B, C, and D are not correct. Exhaustive and mutually exclusive refer to events or outcomes, not types of variables. Complementary and cumulative describe different methods of calculating probabilities, not types of variables. Real and unreal are not terms used to categorize random variables.

Question 7

A discrete probability distribution:
A) is a set of possible values and a corresponding set of probabilities that sum to 1
B) is a modeling tool that can be used to incorporate uncertainty into models
C) can be estimated from long-run proportions
D) is the distribution of a single random variable

Accepted Answer

A discrete probability distribution is defined as a set of possible values and a corresponding set of probabilities that sum to 1. This means that for every possible outcome, there is a probability assigned to it, and the sum of all probabilities equals 1.

Question 8

(A) What is the expected completion time (in months) from now for this project?
(B) How much variability (in months) exists around the expected value found in (A)?

Accepted Answer

The answer of (A) What is the expected completion time...

Question 9

Find the probability distribution of X.

Accepted Answer

The answer of Find the probability distribution of X....

Question 10

What is the probability that this project will be completed in less than 4 months from now?

Accepted Answer

The answer of What is the probability that this project...

Question 11

A small grocery store is considering installing an express checkout line. Let X be the number of customers in the regular checkout line. Note that these numbers include the customers being served, if any. The probability distribution of X is given in the table below. 
-Find the probability that no more than one customer is in line.

Accepted Answer

The answer of A small grocery store is considering installing...

Question 12

The number of cars produced by GM during a given quarter is a continuous random variable.

Accepted Answer

The number of cars produced by GM is a discrete random variable since it can only take on certain values (whole numbers) and not any value within a range.

Question 13

A small grocery store is considering installing an express checkout line. Let X be the number of customers in the regular checkout line. Note that these numbers include the customers being served, if any. The probability distribution of X is given in the table below. 
-Find the probability that one customer is in the regular checkout line.

Accepted Answer

The answer of A small grocery store is considering installing...

Question 14

The number of car insurance policy holders is an example of a discrete random variable.

Accepted Answer

The number of car insurance policy holders takes on a countable number of possible values (i.e. 0, 1, 2, 3, etc.), which is a characteristic of a discrete random variable.

Question 15

What is the probability that this project will not be completed on time?

Accepted Answer

The answer of What is the probability that this project...

Question 16

The temperature of the room in which you are writing this test is a continuous random variable.

Accepted Answer

Temperature can take on any value within a certain range, and therefore is a continuous random variable.

Question 17

The possible annual percentage return of the stocks of Gamma, Inc. and Delta, Inc. share a common probability distribution, given below. 
-(A) What is the expected annual return of each stock?
(B) What is the standard deviation of the annual return of each stock?
(C) On the basis of your answers to (A) and (B), which of these stocks would you prefer to buy? Defend your choice.
(D) Are the annual returns of these two stocks positively or negatively associated with each other? How might the answer to this question influence your decision to purchase shares?

Accepted Answer

The answer of The possible annual percentage return of the...

Question 18

If a new pipeline will be constructed in the event that all three wells are successful, what is the probability that the pipeline will be constructed?

Accepted Answer

The answer of If a new pipeline will be constructed...

Question 19

A small grocery store is considering installing an express checkout line. Let X be the number of customers in the regular checkout line. Note that these numbers include the customers being served, if any. The probability distribution of X is given in the table below. 
-Find the probability that at least two people are in line.

Accepted Answer

The answer of A small grocery store is considering installing...

Question 20

The number of people entering a shopping mall on a given day is an example of a discrete random variable.

Accepted Answer

The number of people entering a shopping mall can only take on specific, separate values (e.g., 1, 2, 3, ... people), which fits the definition of a discrete random variable.

Quiz 4: Probability and Probability Distributions

​A probability tree is a graphical representation of how events occur through time, which is useful for calculating probabilities.

Find the probability that three or fewer customers are in line.

If it costs $200,000 to drill each well and a successful well will produce $1,000,000 worth of oil over its lifetime, what is the expected net value of this three-well program if no wells are successful?

The time students spend in a computer lab during one day is an example of a continuous random variable.

If it costs $200,000 to drill each well and a successful well will produce $1,000,000 worth of oil over its lifetime, what is the expected net value of this three-well program if all three wells are successful?

There are two types of random variables, they are:

A discrete probability distribution:

(A) What is the expected completion time (in months) from now for this project? (B) How much variability (in months) exists around the expected value found in (A)?

Find the probability distribution of X.

What is the probability that this project will be completed in less than 4 months from now?

The number of cars produced by GM during a given quarter is a continuous random variable.

The number of car insurance policy holders is an example of a discrete random variable.

What is the probability that this project will not be completed on time?

The temperature of the room in which you are writing this test is a continuous random variable.

If a new pipeline will be constructed in the event that all three wells are successful, what is the probability that the pipeline will be constructed?

The number of people entering a shopping mall on a given day is an example of a discrete random variable.

A probability tree is a graphical representation of how events occur through time, which is useful for calculating probabilities.