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 result in an auto accident. Assume that the cost of an accident can be modeled with a beta distribution with an alpha parameter of 2, a beta parameter of 3, a minimum value of $300, and a maximum value of $18,000. 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 (in $) resulting from accidents? (Use at least 1,000 trials. Round your answer to two decimal places.)

$

Estimate the variance of the cost resulting from accidents. (Round your answer to the nearest integer.)

Provide a 95% confidence interval (in $) on this mean. (Round your answers to two decimal places.)

$

to $

(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? (Use at least 1,000 trials. Round your answer to three decimal places.)

Provide a 95% confidence interval on this proportion. (Round your answers to three decimal places.)