an insurance company's losses of a particular type per year are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of $50 million. Assum the risk taken on by the insurance company are entriely nonsystematic. The one year risk free rate is 5% per annum with annual compounding. Estimate the cost of the following

a) A contract that will pay in one year time 60% of the insurance company's costs on a pro rata analysis

b) A contract thay pays $100 million in one year's time if losses exceed $200 million