In Problem 11, suppose that the damage amount is triangularly distributed with parameters 500, 1500, and 7000. That is, the damage in an accident can be as low as $500 or as high as $7000, the most likely value is $1500, and there is definite skewness to the right. (It turns out, as you can verify in RISKview, that the mean of this distribution is $3000, the same as in Problem 11.) Use @RISK to simulate the amount you pay for damage. Run 5000 iterations. Then answer the following questions. In each case, explain how the indicated event would occur.
a. What is the probability that you pay a positive amount but less than $250?
b. What is the probability that you pay more than $500?
c. What is the probability that you pay exactly $1000 (the deductible)?
Problem 11
Suppose you own an expensive car and purchase auto insurance. This insurance has a $1000 deductible, so that if you have an accident and the damage is less than $1000, you pay for it out of your pocket. However, if the damage is greater than $1000, you pay the first $1000 and the insurance pays the rest. In the current year, there is probability 0.025 of your having an accident. If you have an accident, the damage amount is normally distributed with mean $3000 and standard deviation $750.
a. Use Excel and a one-way data table to simulate the amount you have to pay for damages to your car. Run 5000 iterations. Then find the average amount you pay, the standard deviation of the amounts you pay, and a 95% confidence interval for the average amount you pay. (Note that many of the amounts you pay will be 0 because you have no accident.)
b. Continue the simulation in part a by creating a two-way data table, where the row input is the deductible amount, varied from $500 to $2000 in multiples of $500. Now find the average amount you pay, the standard deviation of the amounts you pay, and a 95% confidence interval for the average amount you pay for each deductible amount.
c. Do you think it is reasonable to assume that damage amounts are normally distributed? What would you criticize about this assumption? What might you suggest instead?