An insurance companys losses of a particular type per year are to a reasonable approximation normally distributed with a mean of $150million and a standard deviation of $50 million. (Assume that the risks taken on by the insurance company are entirely nonsystemic). The one year risk-free rate is 5% per annum with annual compounding. Estimate the cost for the following:

a. A contract that will pay in one-years time 60% of the insurance companys costs on a pro rata basis.

I don't understand what formulato use to figure this out. Can you explain the formula and how each step is calculated?

b. A contract that pays $100million in one-years time if losses exceed $200million.