Question 1

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

Accepted Answer

A continuous probability distribution is characterized by the fact that its possible values form a continuum, meaning they can take on any value within a given range, rather than being limited to discrete, separate values.

Question 2

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

Accepted Answer

These numbers are generated through deterministic algorithms, making them pseudorandom rather than truly random, as their sequence can be predicted if the algorithm and seed value are known.

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.

Accepted Answer

First, identifying the correct family of distributions (e.g., normal, exponential, binomial) based on the characteristics of the data or process being modeled is crucial. Then, within that family, selecting the specific distribution (e.g., standard normal vs. non-standard normal) that best fits the data or process characteristics ensures the simulation model accurately represents the real-world scenario.

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.

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 5

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

Accepted Answer

Stock prices cannot be negative, which means the distribution used to model them cannot assign a probability to negative values, making an unbounded symmetric probability distribution inappropriate.

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.

Accepted Answer

A discrete distribution is indeed useful for modeling situations where the variable of interest takes on discrete values (such as counting occurrences) or when a continuous variable is approximated discretely for simplification or computational convenience.

Question 7

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

Accepted Answer

A binomial distribution is used to model the number of successes in a fixed number of trials where each trial has two possible outcomes (success or failure) and the probability of success is constant.

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 is a software tool that integrates with Microsoft Excel to perform risk analysis by allowing users to define uncertainty in spreadsheet models through probability distributions for various inputs and then simulates thousands of possible scenarios using Monte Carlo simulation.

Question 9

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

Accepted Answer

Choosing between a symmetric and skewed distribution often depends on the realism of the distribution in representing real-world data. Symmetric distributions are used when data is evenly spread around a central point, while skewed distributions are chosen to represent data that leans towards one side, reflecting more accurately the nature of certain datasets.

Question 10

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

Accepted Answer

The flaw of averages highlights how using average inputs in deterministic models can lead to incorrect or misleading results because it ignores variability and uncertainty in the inputs.

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.

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 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, defined by a minimum, maximum, and mode, is often used in simulations when data is limited or when a more intuitive approach is needed for estimating probability distributions, making it more flexible in certain scenarios compared to the symmetric and more complex 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.

Accepted Answer

The uniform distribution is characterized by having a constant probability for all outcomes within a specified range (between a minimum and a maximum), making all values between these two extremes 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.

Accepted Answer

Simulation models often incorporate random numbers to simulate variability and uncertainty in one or more input variables, reflecting real-world unpredictability, unlike standard spreadsheet models which typically use fixed values for all inputs.

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.

Accepted Answer

@RISK is a risk analysis software that uses Monte Carlo simulation to analyze the risk and uncertainty in models. It automatically collects statistics like averages and standard deviations and can generate various graphs, including histograms, based on the simulation results in the output cells.

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

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.

Accepted Answer

Simulation models allow managers to explore the potential impacts of various decisions or changes in a virtual environment, thus avoiding the costs and risks associated with making those changes in the real world.

Question 18

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

Accepted Answer

This approach can simplify calculations and models, especially when dealing with large sample sizes or when the discrete values can approximate a continuous distribution closely enough for practical purposes.

Question 19

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 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.

Accepted Answer

The binomial distribution indeed models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Quiz 15: Introduction to Simulation Modeling