Question 1

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

This statement is true. It is standard practice to estimate the mean of a distribution using the average of simulated observations, and a confidence interval can be used to indicate the accuracy of the estimate.

Question 2

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 mean to obtain an approximate 95% confidence interval.

Question 3

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

Different random numbers generated by the computer are probabilistically independent, meaning that generating a random number in one cell does not affect the values of any other random numbers generated in the spreadsheet.

Question 4

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 a probability distribution with a triangular shape and is often used in simulation models because it allows for more flexibility in representing uncertain variables with limited data. It is also more intuitive than the normal distribution because it reflects a bounded range of possible outcomes. However, it should be noted that the choice of which distribution to use ultimately depends on the specific circumstances and assumptions of the model.

Question 5

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

Accepted Answer

The flaw of averages refers to the fact that using an average value to represent a diverse population can be misleading, as individuals within that population may have vastly different characteristics and experiences. This can lead to deterministic models that rely on averages producing inaccurate results.

Question 6

@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 allow for the introduction of uncertainty into a spreadsheet model by incorporating probability distributions and simulation of random values.

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

The description correctly describes the binomial distribution.

Question 8

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 9

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

Accepted Answer

The statement accurately describes the function of RISKSIMTABLE in @Risk.

Question 10

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 is true because a narrow confidence interval indicates that the sample mean is a more precise estimate of the true population mean. This is important because it allows analysts to make more informed decisions and draw more accurate conclusions based on the simulation results.

Question 11

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

@Risk does keep statistics and create graphs based on the output cells in the simulation model.

Question 12

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 13

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. Selecting the appropriate family of probability distribution is the first step, and then selecting the appropriate member (e.g. normal distribution, lognormal distribution, etc.) within that family is the second step.

Question 14

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

Accepted Answer

Modeling a random stock price with an unbounded symmetric probability distribution would result in unrealistic probabilities of extreme price movements. Stock prices are typically modeled using bounded distributions such as the lognormal distribution.

Question 15

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 16

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 17

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 in spreadsheet simulations allow for easy replication of key results by varying input values and seeing how they affect output. This is useful for testing different scenarios and making predictions based on the simulation.

Question 18

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

Discrete distribution is useful in situations where the uncertain quantity is not continuous or a discrete approximation to a continuous variable is desired.

Question 19

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 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