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Suppose you own an expensive car and purchase auto insurance. This insurance has a $1000 excess, that is, if you have an accident and the damage is less than $1000, you pay it out of your pocket. However, if the damage is greater than $1000, you pay the excess amount and the insurance pays the rest. In the current year, there is a probability of 0.025 that you will have an accident. It is assumed that the damage amount is normally distributed with a mean of $3000 and a standard deviation of $750.
a) Use Excel to simulate the amount you must pay for damages to your car. Run 500 iterations. Draw suitable graphs, a summary of the data, and comment.
b) Continue the simulation in part (a) by creating a two-way data table giving the amount you pay, for different excess payable ranging 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 excess payable considered. Comment on your findings.
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