Deck 15: Introduction to Simulation Modeling

Question 1

A probability distribution is continuous if its possible values fall along some continuum.

Answer 1

True

Question 2

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

Answer 2

True

Question 3

When determining the most appropriate input probability distribution in a simulation model,first select the most appropriate family,and then select the most appropriate member of that family.

Answer 3

True

Question 4

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.

Question 5

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

Question 6

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

Question 7

A random number from a binomial distribution indicates the number of successes in a certain number of identical trials.

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.

Question 9

We typically choose between a symmetric and skewed distribution on the basis of realism.

Question 10

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

Question 11

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.

Question 12

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

Question 13

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

Question 14

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.

Question 15

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.

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.

Question 17

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

Question 18

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

Question 19

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

Question 20

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 where we want to generate the random number of successes in the n trials.

Question 21

The "building blocks" of all spreadsheet simulation models are

A)deterministic inputs.
B)random numbers between 0 and 1.
C)decision variables.
D)probability distributions for uncertain input variables.

Question 22

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

Question 23

Simulation models are particularly useful for

A)forecasting.
B)obtaining deterministic outputs.
C)evaluating constraints.
D)asking what-if questions.

Question 24

Each different set of values obtained for the uncertain quantities in a simulation model are considered to be

A)the mean of the probability distribution.
B)a scenario.
C)a best guess.
D)a trial.

Question 25

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

Question 26

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

Question 27

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.

Question 28

In general,important characteristics of probability distributions include the following distinctions

A)discrete versus continuous.
B)symmetric versus skewed.
C)bounded versus unbounded.
D)all of these choices.

Question 29

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.

Question 30

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

Question 31

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.

Question 32

Which of the following statements is correct regarding the graph of a discrete probability distribution?

A)It is a series of spikes.
B)The height of each spike is the probability of the corresponding value.
C)There is an empty space between adjacent spikes.
D)All of these statements are correct.

Question 33

Assume that x is a random number between 0 and 1,and that the number of units expected to be sold is uniformly distributed between 300 and 500.In this case,sales are given by the expression

A)300 + x.
B)500 - x.
C)300 + 200 x.
D)500 - 200 x.

Question 34

Which statement is true regarding a simulation model?

A)It makes decision-making easier.
B)It explicitly incorporates uncertainty in one or more input variables.
C)It does not require any best guesses.
D)It always uses a normal probability model.

Question 35

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.

Question 36

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.

Question 37

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.

Question 38

Which of the following statements are false regarding the graph of a continuous probability distribution?

A)It is characterized by a density function,a smooth curve.
B)It is a series of spikes.
C)The height of the density curve above any point is not actually a probability-that is,it is not necessarily between 0 and 1.
D)Heights above the density function indicate relative likelihoods but are not necessarily values between 0 and 1.

Question 39

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 distribution.

Question 40

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.

Question 41

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.

Question 42

Which of the following statements are false?

A)A probability distribution is discrete if it has a finite number of possible values.
B)A probability distribution is continuous if its possible values fall along some continuum.
C)An example of a discrete probability distribution is the amount of rain that falls during the month of June in Michigan.
D)An example of a continuous distribution is the amount of time it takes for a person calling into a call center to reach a representative.

Question 43

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 statements are true.

Question 44

Which statement is true regarding the triangular distribution?

A)It is a discrete distribution with the minimum and maximum and most likely values.
B)It is more flexible and intuitive than the normal distribution.
C)It is a skewed right distribution.
D)It is a skewed left distribution.

Question 45

Suppose you run a simulation model several times with different order quantities.What can we infer about the quantity that maximizes the output,the company's profit?

A)This quantity is the optimal order quantity.
B)This quantity might be the optimal order quantity,but we also need to consider the company's attitude toward risk.
C)This is not necessarily the optimal order quantity,because it may have produced the largest profit by luck.
D)We cannot infer anything about the quantity.

Question 46

A continuous probability distribution is characterized by a

A)symmetric shape.
B)series of spikes.
C)density function.
D)bounded shape.

Question 47

Which of the following statements are true?

A)A probability distribution is symmetric (around some point)if the distribution to the left of the point is a mirror image of the distribution to the right of the point.
B)We say a distribution is skewed to the right (or positively skewed)if the "longer tail" is the right tail.
C)We say a distribution is skewed to the left (or negatively skewed)if the "longer tail" is the left tail.
D)All of these choices are correct.

Question 48

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)a bell curve.

Question 49

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)Exponential distribution

Question 50

Discrete distributions are sometimes used as approximations of continuous distributions

A)because they are more accurate.
B)because they are simpler.
C)when the mean and variance of the distribution are unknown.
D)when the shape of the continuous distribution is not symmetric.

Question 51

Which statement 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)It models bimodal distributions well.

Question 52

If we want to model the time it takes to serve a customer at a bank,we will probably choose a(n)_____ distribution.

A)symmetric
B)positively skewed
C)negatively skewed
D)unbounded

Question 53

If you add several normally distributed random numbers,the result is normally distributed,where the mean of the sum is the sum of the individual means,and the variance of the sum is the sum of the individual variances.This result is difficult to prove mathematically,but it is easy to demonstrate with simulation.To do so,run a simulation where you add three normally distributed random numbers,each with mean 100 and standard deviation 10.Your single output variable should be the sum of these three numbers.Verify with @RISK that the distribution of this output is approximately normal with mean 300 and variance 300 (hence,standard deviation = 17.32).

Question 54

If we want to model the monthly return on a stock,a good option would be a:

A)symmetric distribution around 0.
B)positively skewed distribution.
C)negatively skewed distribution.
D)bimodal distribution.

Question 55

Many companies have used simulation to determine which of several possible investment projects they should choose.This is often referred to as

A)risk analysis.
B)@RISK investment.
C)unbounded risk.
D)risk management.

Question 56

It is simple to generate a uniformly distributed random number with a minimum and maximum other than 0 and 1.For example,the formula = 150+100 RAND()generates a number uniformly distributed between

A)100 and 150.
B)150 and 250.
C)50 and 100.
D)50 and 250.

Question 57

A probability distribution is bounded if there are values A and B such that

A)A and B represent the 95% confidence interval.
B)A and B are the mean and standard deviation,respectively.
C)A and B are the mean and variance,respectively.
D)no value can be less than A or greater than B.

Question 58

One important special case of bounded distributions is when the only possible values are

A)zero or one.
B)uniformly distributed around the mean.
C)skewed to the right.
D)nonnegative.