Q&A Hero

Q: Although we can determine the optimal bid and the expected profit from that bid in a bidding simulation, we usually cannot determine the probability of winning.

Q: In bidding models, the simulation input variable is the number of competitors who will bid.

Q: The primary objective in simulation models of bidding for contracts is to determine the optimal bid.

Q: Simulation applications involving games of chance are primarily for learning the background of simulation (e.g., modeling gambling casinos of Monte Carlo), since they are not business applications per se.

Q: In a marketing and sales model, which of the following might be a good choice for a discrete distribution to model the random timing of sales? a. RAND() b. Normal distribution c. Binomial distribution d. Exponential distribution e. Poisson distribution

Q: The main issue in marketing and sales models is: a. the amount invested in marketing b. the timing of marketing c. the profit from sales d. the timing of sales e. the tradeoff between marketing and sales

Q: A key input variable in many marketing models of customer loyalty is the: a. Mean profit per customer b. Number of customers c. Churn rate d. Time horizon e. All of these options

Q: Which of the following are not among the marketing applications of simulation? a. The entry of new brands into the market b. Customer preferences for different attributes of products c. Brand-switching behavior of customers d. The effect of advertising on sales e. None of these options

Q: In investment models, a useful approach for generating future returns and inflation factors from historical data is: a. the NPV approach b. the scenario approach c. the averaging approach d. the trend analysis approach e. None of these options

Q: In cash flow models, we are typically interested in investigating: a. the value at risk (VAR) b. the net present value (NPV) c. the amount of loans required to maintain a minimum cash balance d. the interest on loans taken out by a firm e. None of these options

Q: Suppose we compare the difference between the NPV of a financial model in which the means are entered for all input random variables and the NPV of a financial model in which the most likely values are entered for all input random variables. If we see a large difference between the NPV's, this illustrates: a. the value at risk (VAR) b. the effect of randomness c. the flaw of averages d. the bias of the analyst e. None of these options

Q: The amount of variability of a financial output caused by different inputs can be investigated using: a. the NPV function b. a histogram of the NPV c. a tornado chart of NPV d. the value at risk (VAR) e. All of these options

Q: The value at risk (VAR) is typically defined as the: a. 5th percentile of NPV distribution b. 10th percentile of NPV distribution c. 50th percentile of NPV distribution d. 90th percentile of NPV distribution e. 95th percentile of NPV distribution

Q: Financial analysts often investigate the value at risk (VAR) with simulation models. VAR is an indicator of: a. how much to bid for a project b. the expected amount of loss for a project c. what is nearly the worst possible outcome for a project d. the required amount of investment required for a project e. None of these options

Q: Which of the following is among the questions that financial analysts try to answer with simulation models? a. Mean and variance of a project NPV b. Probability that a project with have a negative NPV c. Probability that a company will have to borrow a certain amount during the next year d. Mean and variance of a company's profit during the next fiscal year e. All of these options

Q: Which of the following is not among the financial applications where simulation can be applied? a. Future stock prices b. Customer preferences for different attributes of products c. Future interest rates d. Future cash flows e. None of these options

Q: Which of the following @RISK functions can be used to find the probability of a particular value in an output distribution? a. RISKMIN b. RISKMAX c. RISKPERCENTILE d. RISKTARGET e. None of these options

Q: Which of the following functions is not an @RISK statistical function? a. RISKMIN b. RISKMAX c. RISKPERCENTILE d. RISKSIMTABLE e. None of these options

Q: Which of the following functions is often required in simulations where we must model a process over multiple time periods and must deal with uncertain timing of events? a. RISKMIN b. RISKMAX c. NPV d. IF e. None of these options

Q: Which of the following distributions is most likely to be used to develop a simulation model for estimating the time until failure of a product in a simulation model? a. Binomial b. Gamma c. Normal d. Chi-square

Q: In a manufacturing model, we might simulate the number of days to produce a batch and the yield from each batch. The number of days would typically be a ___________ distribution and the yield would be a ___________ distribution. a. Continuous, discrete b. Continuous, continuous c. Discrete, continuous d. Discrete, discrete

Q: Which of the following functions is not appropriate in cases where we run a single simulation? a. RISKMIN b. RISKMAX c. RISKPERCENTILE d. RISKSIMTABLE e. None of these options

Q: In a warranty cost modeling model, which of the following is a key input random variable? a. Warranty cost b. Warranty time limitation c. Lifetime of product d. Replacement cost of product e. All of these options

Q: Suppose we have a 0-1 output for whether a bidder wins a contract in a bidding model (0=bidder does not win contract, and 1=bidder wins contract). From the mean of this output we can tell: a. the number of times the bidder wins the contract b. the number of times the bidder does not win the contract c. the probability that the bidder will win the contract d. the probability that the bidder will not win the contract e. None of these options

Q: The two random variables we typically simulate as inputs in bidding models are? a. Number of bidding competitors and bid amount b. Number of bidding competitors and bid profit c. Individual bid amounts and net bidding profits d. Mean number of bidding competitors and net bidding profit e. None of these options

Q: Customer loyalty models are an example of which of the following types of simulation application? a. Operations models b. Financial models c. Marketing models d. Games of chance e. None of these options

Q: Cash balance models are an example of which of the following types of simulation application? a. Operations models b. Financial models c. Marketing models d. Games of chance e. None of these options

Q: Bidding for contracts is an example of which of the following types of simulation model application? a. Operations models b. Financial models c. Marketing models d. Games of chance e. None of these options

Q: Which of the following is typically not an application of simulation models? a. Operations models b. Financial models c. Marketing models d. Value of Information models e. None of these options

Q: The executive also fairly confident that the company really wants to hire her, and she thinks she may be able to negotiate a lower strike price ($40) and a larger number of shares in the option (3,00 shares). What would be the value of the options in that case?

Q: NARRBEGIN: SA_111_116An oil company is trying to determine the amount of oil that it can expect to recover from an oil field. The unknowns are: the area of the field (in acres), the thickness of the oil-sand layer, and the primary recovery factor (in barrels per acre per foot of thickness). Based on geological information, the following probability distributions have been estimatedEstimate of Productive Area Acres Probability 9,000 0.05 10,000 0.10 11,000 0.15 12,000 0.35 13,000 0.25 14,000 0.10Estimate of Pay Thickness Smallest Value: 15 ft Most Likely Value: 50 ft Largest Value: 120 ft Estimate of Primary Recovery Minimum Value: 20 bbl./acre-ft Maximum Value: 90 bbl./acre-ftThe amount of reserves that can be produced is then the product of the area, thickness, and recovery factor:Number of barrels = Productive Area x Pay Thickness x Primary Recovery FactorNARREND(A) Use @RISK distributions to generate the three random variables and derive a distribution for the amount of reserves. What is the amount we can expect to recover from this field?(B) The production output is a product of three very different types of input distributions. What does the output distribution look like? What are the implications of the shape of this distribution?(C) What is the standard deviation of the recoverable reserves? What are the 5th and 95th percentiles of this distribution? What does this imply about the uncertainty in estimating the amount of recoverable reserves?(D) Suppose you think oil price is normally distributed with a mean of $65 per barrel and a standard deviation of $10. How much revenue do you expect the field produce (ignore discounting)?(E) Finally, your engineer is uncertain about costs to drill wells to develop the field, but she thinks the most likely cost will be $1.7Bn, although it could be as much as $3Bn or as little as $1Bn. What is your expected profit from the field?(F) What is the chance that you will loose money? Is this a risky venture?

Q: NARRBEGIN: SA_104_110A fine arts institute is planning a summer camp where it will host young musicians from around the country one year from now. Within the next two weeks, the organizers must decide how many violins to reserve with the company that will provide instruments. On one hand, they do not want to reserve too few violins because if they end up with more applicants than instruments available, they will have to turn applicants away. On the other hand, they do not want to reserve too many violins because they pay a non-refundable cost of $500 for each violin reserved. Based on historical data, the institute believes that the potential number of camp participants has a normal distribution with mean 600 and standard deviation 100. Each potential camp participant pays an $895 fee that covers all costs, including the instrument rental.NARREND(A) Use a simulation model to help the institute decide how many violins they must reserve with the instrument company. Consider five different possible reservation quantities: 400, 500, 600, 700, 800. Which of these quantities yields the highest total revenue, net of instrument costs?(B) Which simulation yields the largest median total revenue?(C) Which simulation has the most risk as measured by spread or dispersion in the data? Please state clearly what statistic you used to answer this question.(D) Are there any simulations in which there is at least a 1 in 20 (i.e., 5%) chance of getting a negative total revenue? Briefly explain in one sentence.(E) For each simulation what is the probability of exceeding $175,000 in total revenue (approximate these numbers as closely as possible from the data given in the above table). Please put your answer in the following table:Simulation 1Simulation 2Simulation 3Simulation 4Simulation 5 (F) Considering your answers for (A) through (E), please state how many instruments you think should be reserved in advance and explain why.(G) Suppose the institute is able to negotiate with the instrument company to reduce the cost for a violin from $500 to $350. Re-run the simulation model using the same reservation quantities (but with $350 for the unused instrument cost). Has the reservation quantity that yields the highest average revenue changed? If so, please explain why this has occurred.

Q: NARRBEGIN: SA_99_103Suppose you are going to invest equal amounts in three stocks. The annual return from each stock is normally with mean 0.01 (1%) and standard deviation 0.06. The annual return on your portfolio, the output variable of interest, is the average of the three stock returns. Run @RISK, using 1000 iterations, on each of the scenarios described in the questions below, and report few results from the summary report sheets.NARREND(A) The three stock returns are highly correlated. The correlation between each pair is 0.9(B) The three stock returns are practically independent. The correlation between each pair is 0.1(C) The first two stocks are moderately correlated. The correlation between their returns is 0.4. The third stock's return is negatively correlated with the other two. The correlation between its return and each of the first two is -0.8.(D) Compare the portfolio distributions from @RISK for the three scenarios in (A), (B) and (C). What do you conclude?(E) You might think of a fourth scenario, where the correlation between each pair of returns is a large negative number such as -0.80. But explain intuitively why this makes no sense. Try running a simulation with these negative correlations to see what happens.

Q: NARRBEGIN: SA_96_98A company produces six-packs of soda cans. Each can is supposed to contain at least 12 ounces of soda. If the total weight in a six-pack is under 72 ounces, the company is fined $100 and receives no sales revenue for the six-pack. Each six-pack sells for $3.00. It costs the company $0.02 per ounce of soda put in the cans. The company can control the mean fill rate of its soda-filling machines. The amount put in each can by a machine is normally distributed with standard deviation 0.10 ounce.NARREND(A) Assume that the weight of each can in a six-pack has a 0,8 correlation with the weight of the other cans in the six-pack. What mean fill quantity (within 0.05 ounce) maximizes expected profit per sic-pack?(B) If the weights of the cans in the six-pack are probabilistically independent, what mean fill quantity (within 0.05 ounce) will maximize expected profit per six-pack?(C) How can you explain the difference in the answers for (A) and (B)?

Q: NARRBEGIN: SA_93_95After Michigan State University reached the final four in the 2000 NCAA Basketball Tournament, a sweatshirt supplier in Lansing is trying to decide how many sweatshirts to print for the upcoming championships. The final four teams (Michigan State, Florida, Wisconsin, and North Carolina) have emerged from the quarterfinal round, and there is a week left until the semifinals, which are then followed in a couple of days by the finals. Each sweatshirt costs $12 to produce and sells for $24. However, in three weeks, any leftover sweatshirts will be put on sale for half price, $12. The supplier assumes that the demand (in thousands) for his sweatshirts during the next three weeks, when interest is at its highest, follows the probability distribution shown in the table below. The residual demand, after the sweatshirts have been put on sale, also has the probability distribution shown in the table below. The supplier realizes that every sweatshirt sold, even at the sale price, yields a profit. However, he also realizes that any sweatshirts produced but not sold must be thrown away, resulting in a $12 loss per sweatshirt.Demand distribution at regular priceDemand distribution at reduced priceDemandProbabilityDemandProbability70.0520.280.130.390.2540.2100.350.15110.260.1120.170.05NARRENDUse @Risk simulation add-in to analyze the sweatshirt sales. Do this for normal distributions, where we assume that the regular demand is normally distributed with mean 10,000 and standard deviation 1500, and that the demand at the reduced price is normally distributed with mean 5,000 and standard deviation 1500.

Q: NARRBEGIN: SA_93_95After Michigan State University reached the final four in the 2000 NCAA Basketball Tournament, a sweatshirt supplier in Lansing is trying to decide how many sweatshirts to print for the upcoming championships. The final four teams (Michigan State, Florida, Wisconsin, and North Carolina) have emerged from the quarterfinal round, and there is a week left until the semifinals, which are then followed in a couple of days by the finals. Each sweatshirt costs $12 to produce and sells for $24. However, in three weeks, any leftover sweatshirts will be put on sale for half price, $12. The supplier assumes that the demand (in thousands) for his sweatshirts during the next three weeks, when interest is at its highest, follows the probability distribution shown in the table below. The residual demand, after the sweatshirts have been put on sale, also has the probability distribution shown in the table below. The supplier realizes that every sweatshirt sold, even at the sale price, yields a profit. However, he also realizes that any sweatshirts produced but not sold must be thrown away, resulting in a $12 loss per sweatshirt.Demand distribution at regular priceDemand distribution at reduced priceDemandProbabilityDemandProbability70.0520.280.130.390.2540.2100.350.15110.260.1120.170.05NARRENDUse @Risk simulation add-in to analyze the sweatshirt sales. Do this for the discrete distributions given in the problem.

Q: NARRBEGIN: SA_93_95After Michigan State University reached the final four in the 2000 NCAA Basketball Tournament, a sweatshirt supplier in Lansing is trying to decide how many sweatshirts to print for the upcoming championships. The final four teams (Michigan State, Florida, Wisconsin, and North Carolina) have emerged from the quarterfinal round, and there is a week left until the semifinals, which are then followed in a couple of days by the finals. Each sweatshirt costs $12 to produce and sells for $24. However, in three weeks, any leftover sweatshirts will be put on sale for half price, $12. The supplier assumes that the demand (in thousands) for his sweatshirts during the next three weeks, when interest is at its highest, follows the probability distribution shown in the table below. The residual demand, after the sweatshirts have been put on sale, also has the probability distribution shown in the table below. The supplier realizes that every sweatshirt sold, even at the sale price, yields a profit. However, he also realizes that any sweatshirts produced but not sold must be thrown away, resulting in a $12 loss per sweatshirt.Demand distribution at regular priceDemand distribution at reduced priceDemandProbabilityDemandProbability70.0520.280.130.390.2540.2100.350.15110.260.1120.170.05NARRENDUse simulation to analyze the supplier's problem. Determine how many sweatshirts he should produce to maximize the expected profit.

Q: NARRBEGIN: SA_89_92Suppose that Mrs. Smart invested 25% of her portfolio in four different stocks. The mean and standard deviation of the annual return on each stock are shown in the first table below. The correlations between the annual returns on the four stocks are shown in the second table below.Distributions of returns Mean StdevStock 116%21%Stock 212%13%Stock 325%38%Stock 418%20%Correlation matrixStock 1Stock 2Stock 3Stock 4Stock 110.750.70.6Stock 20.7510.80.5Stock 30.70.810.65Stock 40.60.50.651NARREND(A) Use @Risk with 100 replications, provide a summary statistics of portfolio return; namely, minimum, maximum, mean, and standard deviation.(B) Use your answers to (A) to estimate the probability that Mrs. Smart's portfolio's annual return will exceed 20%.(C) Use your answers to (A) to estimate the probability that Mrs. Smart's portfolio will lose money during the course of a year.(D) Suppose that the current price of each stock is as follows: stock 1: $16; stock 2: $18; stock 3: $20; and stock 4: $22. Mrs. Smart has just bought an option involving these four stocks. If the price of stock 1, six months from now are is $18 or more, the option enables Mrs. Smart to buy, if she desires, one share of each stock for $20 six months from now. Otherwise the option is worthless. For example, if the stock prices six months from now are: stock 1: $18; stock 2: $20; stock 3: $21; and stock 4: $24, then Mrs. Smart would exercise her option to buy stocks 3 and 4 and receive (21- 20) + (24-20) = $5 in each cash flow. How much is this option worth if the risk-free rate is 8%?

Q: NARRBEGIN: SA_85_88 The College of Arts and Sciences at a Midwestern university currently has three parking lots, each containing 160 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, the probability of a lot 1 parking sticker holder showing up is 73%, a lot 2 parking sticker holders showing up is 75%, and a lot 3 parking sticker holder showing up is 77%. NARREND (A) What are the appropriate probability distributions to model the number of faculty members showing up in each lot? (B) Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a parking space. Assume that the number who shows up at each lot is independent of the number who shows up at the other two lots. (C) Suppose that faculty members are allowed to park in any lot. Does this help solve the problem? Why or why not? (D) Suppose that the numbers of faculty who show up at the three lots are correlated, with each correlation equal to 0.80. Does your answer to (C) change? Why or why not?

Q: NARRBEGIN: SA_81_84In August 2009, a car dealer is trying to determine how many 2010 cars to order. Each car ordered in August 2009 costs $16,000. The demand for the dealer's 2010 models has the probability distribution shown in the table below. Each car sells for $21,000. If the demand for 2010 cars exceeds the number of cars ordered in August 2009, the dealer must reorder at a cost of $18,000 per car. Excess cars can be disposed of at $13,000 per car.Cars demandedProbability250.25300.20350.15400.20450.20NARRENDSuppose that the demand for cars is normally distributed with mean of 120 and standard deviation of 20. Use @Risk simulation add-in to determine the "best" order quantity; that is, the one that has the largest expected profit. Using the statistics and/or graphs from @Risk, discuss whether this order quantity would not be considered the "best" by the car dealer.

Q: NARRBEGIN: SA_81_84In August 2009, a car dealer is trying to determine how many 2010 cars to order. Each car ordered in August 2009 costs $16,000. The demand for the dealer's 2010 models has the probability distribution shown in the table below. Each car sells for $21,000. If the demand for 2010 cars exceeds the number of cars ordered in August 2009, the dealer must reorder at a cost of $18,000 per car. Excess cars can be disposed of at $13,000 per car.Cars demandedProbability250.25300.20350.15400.20450.20NARREND(A) Use simulation to determine how many cars the dealer should order in August, 2009 to maximize his expected profit.(B) For the optimal order quantity, find a 95% confidence interval for the expected profit.(C) Why is it important to develop the confidence interval in (B)?

Q: NARRBEGIN: SA_78_80 A company is about to develop and then market a new product. It wants to build a simulation model for the entire process, and one key uncertain input is the development time, which is measured in an integer number of months. For each of the scenarios in the questions below, choose an "appropriate" distribution, together with its parameters, and explain your choice. NARREND Company experts believe the development time will be from 5 to 9 months. They believe that 7 months is twice as likely as either 6 months or 8 months and that either of these latter possibilities is three times as likely as either 5 months or 9 months.

Q: NARRBEGIN: SA_78_80 A company is about to develop and then market a new product. It wants to build a simulation model for the entire process, and one key uncertain input is the development time, which is measured in an integer number of months. For each of the scenarios in the questions below, choose an "appropriate" distribution, together with its parameters, and explain your choice. NARREND Company experts believe the development time will from 5 to 9 months. They believe the probabilities of the extremes (5 and 9 months) are both 10%, and the probabilities will vary linearly from those endpoints to a most likely value at 7 months.

Q: NARRBEGIN: SA_78_80 A company is about to develop and then market a new product. It wants to build a simulation model for the entire process, and one key uncertain input is the development time, which is measured in an integer number of months. For each of the scenarios in the questions below, choose an "appropriate" distribution, together with its parameters, and explain your choice. NARREND Company experts believe the development time will be from 5 to 9 months, but they have absolutely no idea which of these will result.

Q: 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).

Q: NARRBEGIN: SA_74_76 A company is about to develop and then market a new product. It wants to build a simulation model for the entire process, and one key uncertain input is the development cost. For each of the scenarios in the questions below, choose an "appropriate" distribution, together with its parameters, and explain your choice. NARREND (A) Company experts have no idea what the distribution of the development cost is. All they can state is that "we are 90% sure it will be somewhere between $450,000 and $650,000." (B) Company experts can still make the same two statements as in (A), but now they can also state that "we believe the distribution is symmetric and its most likely value is about $550,000." (C) Company experts can still make the same two statements as in (A), but now they can also state that "we believe the distribution is skewed to the right, and its most likely value is about $500,000."

Q: NARRBEGIN: SA_71_73 It is surprising (but true) that if 23 randomly selected people are in the same room, there is about a 50% chance that at least two people will have the same birthday. Suppose you want to estimate the probability that if 30 people are in the same room, at least two of them will have the same birthday. You can proceed as follows: NARREND (A) Generate the "birthdays" of 30 different people, assuming that each person has a 1/365 chance of having a given birthday (call the days of the year 1, 2, 3, ........,365). You can use a formula involving the INT and RAND functions to generate birthdays. (B) Once you have generated 30 people's birthdays, you can tell whether at least two people have the same birthday using Excel's RANK function (i.e., in the case of a tie, two numbers are given the same rank). Do you see any people with the same birthday in your sample? (C) Obtain at least 20 samples of the 30 person group using the F9 key. What do you estimate the probability of finding two people with the same birthday in a sample of 30 people to be?

Q: NARRBEGIN: SA_65_70 Generate a set of 40 random numbers in a column in an Excel spreadsheet by using RAND function. Fix the set of random numbers by copying the column to another column and using the "Paste Special" command with the "Values" option selected. NARREND Obtain another set random numbers by pressing the F9 (recalculate) key. Do your results change significantly? Do the changes match your expectations? Explain your answer.

Q: NARRBEGIN: SA_65_70 Generate a set of 40 random numbers in a column in an Excel spreadsheet by using RAND function. Fix the set of random numbers by copying the column to another column and using the "Paste Special" command with the "Values" option selected. NARREND (A) What fraction of the random numbers are smaller than 0.5? (B) What fraction of the time is a random number less than 0.5 followed by another random number less than 0.5? (C) What fraction of the random numbers are larger than 0.8? (D) What do you expect the answers to (A), (B) and (C) to be before simulating? Do the answers you provided to those questions match your expectations? Explain why or why not. (E) Suppose your answers to (A), (B) and (C) are not close to the expected answers. What can you do to obtain answers from the simulation that are closer to the expected answers?

Q: 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 disbribution.

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

Q: 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.

Q: 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.

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

Q: 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.

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

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

Q: 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.

Q: 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.

Q: 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.

Q: 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.

Q: @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.

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

Q: 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

Q: 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.

Q: 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.

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

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

Q: 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.

Q: 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.

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

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

Q: 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.

Q: We typically choose between a symmetric and skewed distribution on the basis of practical modeling issues.

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

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

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

Q: The Excel RAND() function generates random numbers from a Normal(0,1) distribution.

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

Q: 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.