Question 1

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 different scenarios and make predictions about the potential outcomes without having to make any actual changes to the system. This can save time and resources, while also helping to identify potential problems or opportunities before they occur.

Question 2

When we maximize or minimize the value of a decision variable by running several simulations simultaneously,we have found an optimal solution to the problem and attitude toward risk becomes irrelevant.

Accepted Answer

Finding an optimal solution through simulations does not make attitude toward risk irrelevant; different stakeholders may value the outcomes differently based on their risk preferences, affecting the decision on what is considered "optimal."

Question 3

Data tables in spreadsheet simulations are useful for taking a "prototype" simulation and replicating its key results a desired number of times.

Accepted Answer

Data tables can be used to vary input values and analyze how the output changes, allowing for the replication of key results in the simulation.

Question 4

A probability distribution is continuous if its possible values are essentially some continuum.

Accepted Answer

A continuous probability distribution is one in which the variable can take on any value within a range or interval, giving a continuum of possible values. This includes distributions such as the normal distribution and the uniform distribution. In contrast, a discrete probability distribution has a finite or countably infinite set of possible values, such as the binomial or Poisson distributions.

Question 5

If we want to model a random stock price,we should do so with an unbounded symmetric probability distribution.

Accepted Answer

Stock prices can have extreme values and can even become negative, so an unbounded distribution would not be appropriate. Additionally, stock prices often have a positive skew (i.e. more small gains than small losses, but occasional large losses), so a symmetric distribution would not accurately capture this behavior. A more appropriate distribution for modeling stock prices would be a distribution that allows for skewness and boundedness, such as the lognormal distribution.

Question 6

Analysts often plan a simulation so that the confidence interval for the mean of some important output will be sufficiently narrow.The reasoning is that narrow confidence intervals imply more precision about the estimated mean of the output variable.

Accepted Answer

This statement is true. A narrower confidence interval indicates that the estimated mean is more precise, as it suggests that there is less variability in the data and therefore less uncertainty in estimating the true population mean.

Question 7

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

Accepted Answer

A correlation matrix is always symmetric because the correlation between variable A and variable B is the same as the correlation between variable B and variable A. Therefore, the correlations above the diagonal are a mirror image of those below it.

Question 8

The normal distribution is often used in simulation models because it is the most common distribution in statistics and it does not allow negative values.

Accepted Answer

The normal distribution is commonly used because it describes many natural phenomena well, but it does allow for negative values, as it extends infinitely in both directions along the x-axis.

Question 9

When we run simulation,the @Risk automatically keeps statistics such as averages and standard deviations,and can also create graphs such as histograms based on the values generated in the output cells in the simulation model.

Accepted Answer

This statement is true, as @Risk does keep statistics and can create graphs based on the output of a simulation model.

Question 10

A probability distribution is bounded if there are values A and B such that only one possible value can be less than A or greater than B.

Accepted Answer

A probability distribution is considered bounded if there are values A and B such that no possible values can be less than A or greater than B, meaning all possible values lie within the interval [A, B].

Question 11

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

Accepted Answer

Excel's built-in functions can generate random numbers from various types of probability distributions, including normal, uniform, binomial, and Poisson distributions, among others. The RAND function itself generates random numbers uniformly between 0 and 1.

Question 12

The triangular distribution is sometimes used in simulation models because it is more flexible and intuitive than the normal distribution.

Accepted Answer

The triangular distribution is often used in simulation models because it allows for a range of values between two extremes, with a mode in the center of the range. This makes it more flexible and intuitive than the normal distribution, which assumes a symmetric, bell-shaped curve.

Question 13

Sometimes it is convenient to treat a discrete probability distribution as continuous,and vice versa.

Accepted Answer

It is common to use the approximation of a continuous probability distribution to simplify calculations or modeling, and discrete distributions can often be represented as continuous distributions with small enough intervals. Similarly, continuous distributions can be modeled with discrete approximations, such as using a histogram to discretize the data.

Question 14

A discrete distribution is useful for many situations,either when the uncertain quantity is not really continuous (the number of televisions demanded,for example)or when you want a discrete approximation to a continuous variable.

Accepted Answer

A discrete distribution is indeed useful in situations where the uncertain quantity is not really continuous or when a discrete approximation to a continuous variable is desired.

Question 15

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

Accepted Answer

This is true, as a variable will always show perfect correlation with itself.

Question 16

The "random" numbers generated by the RAND function (or by any other package's random number generator)are not really random.

Accepted Answer

The numbers generated by the RAND function (or any other package's random number generator) are only pseudo-random, meaning they are generated by a deterministic algorithm and can be reproduced if the same seeds are used. True randomness is only achieved through physical processes, such as radioactive decay or atmospheric noise.

Question 17

It is common in computer simulations to estimate the mean of some distribution by the average of the simulated observations.The usual practice is then to accompany this estimate with a confidence interval,which indicates the accuracy of the estimate.

Accepted Answer

It is true that computer simulations often estimate the mean using the average of simulated observations, and it is also common practice to provide a confidence interval to indicate the level of accuracy of the estimate.

Question 18

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

Accepted Answer

RISKSIMTABLE allows users to run multiple simulations simultaneously, each with different input or decision variable settings.

Question 19

The binomial distribution can be well approximated by the normal distribution when the number of trials n is sufficiently small and the probability of success p is not too close to 0 or 1.

Accepted Answer

The binomial distribution can be well approximated by the normal distribution when the number of trials n is sufficiently large and the probability of success p is not too close to 0 or 1, not when n is small.

Question 20

Spreadsheet simulation modeling is quite similar to the other modeling applications in that it begins with input variables and then relates these with appropriate Excel formulas to produce output variables of interest.

Accepted Answer

Spreadsheet simulation modeling does indeed begin with input variables and produce output variables using Excel formulas.

Quiz 15: Introduction to Simulation Modeling