Question 1

Which of the following statements is true regarding the Normal distribution?
A) It is always the appropriate distribution in simulation modeling
B) It does not permit negative values
C) There is a 95% chance that values will be within ± 2 standard deviations of the mean
D) All of these options

Accepted Answer

The Normal distribution is a commonly used distribution in simulation modeling, but it is not always the appropriate distribution. It does not have any constraints on the range of possible values, so it can have negative values. The 68-95-99.7 rule states that there is a 95% chance that values will be within ± 2 standard deviations of the mean for a Normal distribution.

Question 2

Excel's standard functions,along with the RAND function,can be used to generate random numbers from many different types of probability distributions.

Accepted Answer

Excel's standard functions and the RAND function can be used to generate random numbers from various probability distributions such as normal distribution, binomial distribution, Poisson distribution, etc.

Question 3

A common guideline for constructing a 95% confidence interval is to place upper and lower bounds one standard error on either side of the mean.

Accepted Answer

A 95% confidence interval is typically constructed by placing upper and lower bounds 1.96 standard errors on either side of the mean, not just one standard error.

Question 4

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 in Excel models the uniform distribution from 0 to 1.

Question 5

A correlation matrix must always have 1's along its diagonal (because a variable is always perfectly correlated with itself)and numbers between -1 and +1 elsewhere.

Accepted Answer

This statement is true. A correlation matrix will always have 1's along its diagonal because each variable is perfectly correlated with itself. The values between -1 and +1 represent the correlation between two different variables.

Question 6

If x is a random number between 0 and 1,then we can use x to simulate a variable that is uniformly distributed between 100 and 200 using the formula:
A) 100 + x
B) 200 -x
C) 100 + 100x
D) 200x

Accepted Answer

Since we want to simulate a variable that is uniformly distributed between 100 and 200, we need to find a formula that maps the range of [0,1] to [100,200]. The formula that accomplishes this is 100 + 100x, since plugging in 0 yields 100 and plugging in 1 yields 200, and any value in between will be linearly interpolated between those two values.

Question 7

It is usually fairly straightforward 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 is not always straightforward to predict from the shape(s) of the input distribution(s) due to the complexities of the transformations applied, interactions between variables, and the effects of non-linear operations.

Question 8

The primary difference between simulation models and other types of spreadsheet models is that simulation models contain ____:
A) deterministic inputs
B) random numbers
C) output cells
D) constraints

Accepted Answer

Simulation models contain random numbers as they are used to simulate different scenarios and outcomes based on probability distributions. Deterministic inputs, output cells, and constraints can also be present in simulation models, but the primary difference is the incorporation of random numbers.

Question 9

A correlation matrix must always be symmetric,so that the correlations above the diagonal are a mirror image of those below it.

Accepted Answer

This is true because the correlation between variable A and variable B is the same as the correlation between variable B and variable A. Therefore, the matrix must be symmetric.

Question 10

Which of the following is not one of the important distinctions of probability distributions?
A) Discrete versus continuous
B) Symmetric versus skewed
C) Bounded versus unbounded
D) Positive versus negative

Accepted Answer

Positive versus negative is not one of the important distinctions of probability distributions. The other three distinctions (discrete versus continuous, symmetric versus skewed, bounded versus unbounded) are all important in analyzing and interpreting probability distributions.

Question 11

Discrete distributions are sometimes used in place of continuous distributions:
A) because they are more accurate
B) because they are more simple
C) when we don't know the mean and variance of the distribution
D) when we need to generate a histogram

Accepted Answer

The answer of Discrete distributions are sometimes used in place...

Question 12

A distribution for modeling the time it takes to serve a customer at a bank is probably:
A) symmetric
B) left skewed
C) right skewed
D) uniform

Accepted Answer

The time it takes to serve a customer at a bank is likely to be right skewed, as there may be a few customers who take a long time to complete their transactions and many customers who take a much shorter time. This can result in a distribution that is skewed to the right.

Question 13

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 14

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 risk of creating a deterministic model based on the means of uncertain inputs. This can lead to misleading predictions and decisions.

Question 15

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 reasonably large and p isn't too close to 0 or 1, the binomial distribution can be well approximated by the normal distribution. This is known as the normal approximation to the binomial distribution. The mean of the normal distribution is np and the standard deviation is sqrt(np(1-p)).

Question 16

One of the primary advantages of simulation models that they enable managers to answer what-if questions about changes in systems without actually changing the systems themselves.

Accepted Answer

Simulation models allow managers to test out different scenarios and make predictions on how the system would react without the need for actual implementation of changes. This helps to reduce the risk and cost associated with experimenting with real-world systems.

Question 17

RISKSIMTABLE is an @RISK function for running several simulations simultaneously,one for each setting of an input or decision variable.

Accepted Answer

RISKSIMTABLE allows for running multiple simulations with different input or decision variable settings simultaneously.

Question 18

Which of the following statements is true regarding the Triangular distribution?
A) It is a discrete distribution with a minimum,maximum and most likely value
B) It is more flexible and intuitive than the normal distribution
C) It is a symmetric distribution
D) All of these options

Accepted Answer

The Triangular distribution is more flexible and intuitive than the normal distribution because it can model scenarios where information is limited or uncertain, and it allows for the specification of minimum, maximum, and most likely values directly.

Question 19

Correlation between two random input variables may change the mean of an output,but it will not affect the variability and shape of an output distribution.

Accepted Answer

Correlation between two random input variables can affect the variability and shape of an output distribution. Specifically, if the correlation is high, it can decrease the variability (i.e. make the output more clustered around the mean) and change the shape of the distribution from symmetric to skewed.

Question 20

When the value of a decision variable has been optimized by running several simulations,attitude toward risk should no longer be relevant.

Accepted Answer

Attitude toward risk is always relevant because it determines the objective function and constraints used in the simulation optimization process. Even after optimization, the decision maker's attitude toward risk affects their willingness to accept the optimal solution and their preferences for alternative solutions.

Quiz 10: Introduction to Simulation Modeling

Which of the following statements is true regarding the Normal distribution?

Excel's standard functions,along with the RAND function,can be used to generate random numbers from many different types of probability distributions.

A common guideline for constructing a 95% confidence interval is to place upper and lower bounds one standard error on either side of the mean.

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

A correlation matrix must always have 1's along its diagonal (because a variable is always perfectly correlated with itself)and numbers between -1 and +1 elsewhere.

If x is a random number between 0 and 1,then we can use x to simulate a variable that is uniformly distributed between 100 and 200 using the formula:

It is usually fairly straightforward to predict the shape of the output distribution from the shape(s)of the input distribution(s).

The primary difference between simulation models and other types of spreadsheet models is that simulation models contain ____:

A correlation matrix must always be symmetric,so that the correlations above the diagonal are a mirror image of those below it.

Which of the following is not one of the important distinctions of probability distributions?

Discrete distributions are sometimes used in place of continuous distributions:

A distribution for modeling the time it takes to serve a customer at a bank is probably:

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

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:

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?

One of the primary advantages of simulation models that they enable managers to answer what-if questions about changes in systems without actually changing the systems themselves.

RISKSIMTABLE is an @RISK function for running several simulations simultaneously,one for each setting of an input or decision variable.

Which of the following statements is true regarding the Triangular distribution?

Correlation between two random input variables may change the mean of an output,but it will not affect the variability and shape of an output distribution.

When the value of a decision variable has been optimized by running several simulations,attitude toward risk should no longer be relevant.