Question 1

The uniform distribution is bounded by a minimum and a maximum,and all values between these two extremes are equally likely.

Accepted Answer

This is the definition of a uniform distribution.

Question 2

We typically choose between a symmetric and skewed distribution on the basis of practical modeling issues.

Accepted Answer

The choice between symmetric and skewed distributions is often based on the nature of the data and the modeling requirements, such as the presence of outliers or the need for normality in statistical tests.

Question 3

The three parameters required to specify a triangular distribution are the minimum,mean and maximum.

Accepted Answer

The three parameters required to specify a triangular distribution are the minimum, the maximum, and the mode (the peak).

Question 4

When n is reasonably large and p isn't too close to 0 or 1,the binomial distribution can be well approximated by which of the following distributions?
A) Uniform distribution
B) Normal distribution
C) Triangular distribution
D) None of these options

Accepted Answer

When n is large and p is not too close to 0 or 1, the binomial distribution can be approximated by a normal distribution with mean np and variance np(1-p). This is known as the normal approximation to the binomial distribution.

Question 5

Correlation between two random input variables might not change the mean of an output,but it can definitely affect the variability and shape of an output disbribution.

Accepted Answer

Correlation between two input variables can affect the variability and shape of an output distribution even if it does not change the mean. Correlation measures the strength of the relationship between two variables, and this relationship can impact how the output distribution is shaped and how spread out the values are.

Question 6

The flaw of averages is the reason deterministic models can be very misleading.

Accepted Answer

The flaw of averages is a well-known concept in statistics and highlights the fact that using an average value for a variable can be misleading if there is significant variability or heterogeneity within the data. This can result in incorrect conclusions or decisions being made based on deterministic models that rely on an average value.

Question 7

The binomial distribution is a discrete distribution that is applied to situations where n independent and identical "trials" occur,with each trial resulting in a "success" or "failure," and we want to generate the random number of successes in the n trials.

Accepted Answer

This is an accurate description of the binomial distribution.

Question 8

@Risk introduces uncertainty explicitly into a spreadsheet model by allowing several inputs to have probability distributions and then enabling the simulation of random values from these inputs.

Accepted Answer

@Risk does indeed introduce uncertainty explicitly by allowing users to assign probability distributions to inputs and simulate random values from those inputs through simulation.

Question 9

If a model contains uncertain outputs,it can be very misleading to build a deterministic model by using the means of the inputs to predict an output.This is called the:
A) Law of Large Numbers.
B) Flaw of Averages
C) Law of Inevitable Disappointment
D) Central Limit Theorem

Accepted Answer

The Flaw of Averages refers to the practice of using mean values of inputs to predict an output in a deterministic model, even when the outputs themselves are uncertain. This can lead to misleading or incorrect predictions, as it is not taking into account the variability and potential extremes of the inputs.

Question 10

A primary difference between standard spreadsheet models and simulation models is that at least one of the input variable cells in a simulation model contains random numbers.

Accepted Answer

Simulation models incorporate the element of randomness in at least one input variable cell to allow for a range of possible outcomes instead of just one calculated result like in standard spreadsheet models.

Question 11

The RAND()function in excel models which of the following probability distributions:
A) Normal(0,1)
B) Uniform(0,1)
C) Normal(-1,1)
D) Uniform(-1,1).

Accepted Answer

The RAND() function models a uniform distribution between 0 and 1, hence the best choice is B, Uniform(0,1).

Question 12

When you try to find the most appropriate input probability distribution in a simulation model,you first have to choose the most appropriate family,and then you have to select the most appropriate member of that family

Accepted Answer

This statement is true. In order to select the most appropriate input probability distribution for a simulation model, first you need to choose the most suitable distribution family such as normal, exponential, uniform, etc. Once you have selected the family, you can then choose the specific member of that family, such as the mean and standard deviation for a normal distribution.

Question 13

The Excel RAND()function generates random numbers from a Normal(0,1)distribution.

Accepted Answer

The Excel RAND() function generates random numbers from a Uniform(0,1) distribution. It does not generate random numbers from a Normal distribution. The NORMINV() and NORMDIST() functions can be used to generate random numbers from a Normal distribution in Excel.

Question 14

Different random numbers generated by the computer are probabilistically dependent.This implies that when we generate a random number in a particular cell,it has some effect on the values of any other random numbers generated in the spreadsheet.

Accepted Answer

Random numbers generated by a computer, especially when using a good random number generator, are designed to be independent of each other. This means the value of one random number does not affect the values of other random numbers generated.

Question 15

A common guideline in constructing confidence intervals for the mean is to place upper and lower bounds one standard error on either side of the average to obtain an approximate 95% confidence interval.

Accepted Answer

A common guideline in constructing confidence intervals for the mean is to place upper and lower bounds 1.96 standard errors on either side of the average to obtain an approximate 95% confidence interval, not just one standard error.

Question 16

A continuous probability distribution is characterized by a:
A) mean and a standard deviation.
B) mean and a variance.
C) density function.
D) histogram

Accepted Answer

Continuous probability distributions are described by a density function. Options A and B require additional calculations from the density function, and option D applies only to discrete distributions.

Question 17

The deterministic (non-simulation)approach,using best guesses for the uncertain inputs,is:
A) better to use in complicated real world applications.
B) a good estimate of what the answer will be using a simulation approach.
C) generally not the appropriate model.
D) the preferred approach when there is correlation between input variables.

Accepted Answer

Deterministic models, which use fixed input values, often do not capture the full range of possibilities and uncertainties inherent in real-world scenarios, making them generally not the most appropriate for complex applications where variability and uncertainty are significant.

Question 18

We can think of the uniform distribution as:
A) the "I have no idea" distribution.
B) a skewed distribution.
C) only modeling positive values.
D) nonnegative.

Accepted Answer

The uniform distribution is often referred to as the "I have no idea" distribution because it assumes all outcomes are equally likely, reflecting maximum uncertainty or lack of information about which outcome will occur.

Question 19

Which of the following statements are true?
A) The @RISK contains a number of functions such as RISKNORMAL and RISKDISCRETE that make it easy to generate observations from the most important probability distributions.
B) You can specify any cell or range of cells in your simulation model as output cells.
When you run the simulation,@RISK automatically keeps summary measures (averages,standard deviation,percentiles,and others)from the values generated in these output cells across the replications.
C) @RISK has a special function,RISKSIMTABLE,which allows you to run the same simulation several times,using a different value of some key input variable each time.
D) All of these options.

Accepted Answer

All of the statements are true. Statement A mentions the functions available in @RISK to generate observations from probability distributions. Statement B explains the output cells and summary measures generated in the simulation. Statement C mentions the RISKSIMTABLE function that allows running the same simulation multiple times with different input variables. Therefore, the correct answer is D.

Question 20

It is usually not too difficult to predict the shape of the output distribution from the shape(s)of the input distribution(s).

Accepted Answer

The shape of the output distribution can be significantly different from the input distribution(s) due to the non-linear transformations and interactions within the model or process being applied, making it challenging to predict without specific analysis.

Quiz 15: Introduction to Simulation Modeling

The uniform distribution is bounded by a minimum and a maximum,and all values between these two extremes are equally likely.

We typically choose between a symmetric and skewed distribution on the basis of practical modeling issues.

The three parameters required to specify a triangular distribution are the minimum,mean and maximum.

When n is reasonably large and p isn't too close to 0 or 1,the binomial distribution can be well approximated by which of the following distributions?

Correlation between two random input variables might not change the mean of an output,but it can definitely affect the variability and shape of an output disbribution.

The flaw of averages is the reason deterministic models can be very misleading.

The binomial distribution is a discrete distribution that is applied to situations where n independent and identical "trials" occur,with each trial resulting in a "success" or "failure," and we want to generate the random number of successes in the n trials.

@Risk introduces uncertainty explicitly into a spreadsheet model by allowing several inputs to have probability distributions and then enabling the simulation of random values from these inputs.

If a model contains uncertain outputs,it can be very misleading to build a deterministic model by using the means of the inputs to predict an output.This is called the:

A primary difference between standard spreadsheet models and simulation models is that at least one of the input variable cells in a simulation model contains random numbers.

The RAND() function in excel models which of the following probability distributions:

When you try to find the most appropriate input probability distribution in a simulation model,you first have to choose the most appropriate family,and then you have to select the most appropriate member of that family

The Excel RAND()function generates random numbers from a Normal(0,1)distribution.

Different random numbers generated by the computer are probabilistically dependent.This implies that when we generate a random number in a particular cell,it has some effect on the values of any other random numbers generated in the spreadsheet.

A common guideline in constructing confidence intervals for the mean is to place upper and lower bounds one standard error on either side of the average to obtain an approximate 95% confidence interval.

A continuous probability distribution is characterized by a:

The deterministic (non-simulation) approach,using best guesses for the uncertain inputs,is:

We can think of the uniform distribution as:

Which of the following statements are true?

It is usually not too difficult to predict the shape of the output distribution from the shape(s)of the input distribution(s).