tatewide Auto Insurance believes that for every trip longer than 10 minutes that

Question

tatewide 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: %

Explanation / Answer

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 a shape1 (alpha) parameter of 1.5, a shape2 (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.
a. If a teenager drives 500 trips longer than 10 minutes, what is the mean cost resulting from accidents?
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?

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