Chapter Review

Appendix 11.1Common Probability Distributions for Simulation

Simulation software such as Analytic Solver, Crystal Ball, or @RISK automates the generation of random values from an even wider selection of probability distributions than is available in native Excel.

Selecting the appropriate probability distribution to characterize a random variable in a simulation model can be a critical modeling decision. In this appendix, we review several probability distributions commonly used in simulation models. We describe the native Excel functionality used to generate random values from the corresponding probability distribution.

Figure 11.32Native Excel Implementation of Custom Discrete Distribution

Figure 11.33Excel Template to Generate Values from a Hypergeometric Distribution

Negative Binomial Distribution

Figure 11.34Excel Template to Generate Values from a Negative Binomial Distribution

Poisson Distribution

Figure 11.35Excel Template to Generate Values from a Poisson Distribution

Problem 11-05 (Risk Analysis for Sanotronics LLC) Question 3 of 9 Check My Work eBook (All answers were generated using 1,000 trials and native Excel functionality.) Statewide Auto Insurance believes that for every trip longer than 10 minutes that a teenager drives, there is a 1 in 1,000 chance that the drive will results in an auto accident. Assume that the cost of an accident can be modeled with a beta distribution with an alpha parameter of 1.5, a beta parameter of 3, a minimum value of $500, and a maximum value of $20,000. Construct a simulation model to answer the following questions. (Hint: Review Appendix 11.1 for descriptions of various types of probability distributions to identify the appropriate way to model the number of accidents in 500 trips.) (a) If a teenager drives 500 trips longer than 10 minutes, what is the average cost resulting from accidents? Round your answer to the nearest whole number. Average Cost: $ Provide a 95% confidence interval on this mean. Round your answers to the nearest whole number. Lower Bound: $ Upper Bound: $ (b) If a teenager drives 500 trips longer than 10 minutes, what is the probability that the total cost from accidents will exceed $8,000? Round your answer to a one decimal percentage. Probability (Accident Cost > $8,000): Provide a 95% confidence interval on this proportion. Round your answers to a one decimal percentage. Lower Bound: % Upper Bound: . Problem 11-05 (Risk Analysis for Sanotronics LLC) Question 3 of 9 Check My Work eBook (All answers were generated using 1,000 trials and native Excel functionality.) Statewide Auto Insurance believes that for every trip longer than 10 minutes that a teenager drives, there is a 1 in 1,000 chance that the drive will results in an auto accident. Assume that the cost of an accident can be modeled with a beta distribution with an alpha parameter of 1.5, a beta parameter of 3, a minimum value of $500, and a maximum value of $20,000. Construct a simulation model to answer the following questions. (Hint: Review Appendix 11.1 for descriptions of various types of probability distributions to identify the appropriate way to model the number of accidents in 500 trips.) (a) If a teenager drives 500 trips longer than 10 minutes, what is the average cost resulting from accidents? Round your answer to the nearest whole number. Average Cost: $ Provide a 95% confidence interval on this mean. Round your answers to the nearest whole number. Lower Bound: $ Upper Bound: $ (b) If a teenager drives 500 trips longer than 10 minutes, what is the probability that the total cost from accidents will exceed $8,000? Round your answer to a one decimal percentage. Probability (Accident Cost > $8,000): Provide a 95% confidence interval on this proportion. Round your answers to a one decimal percentage. Lower Bound: % Upper Bound