A satellite has a life expectancy that follows a normal distribution withmonths andmonths. An insurance company is going to insure the satellite for $500 million.

1. If the satellite is insured for 78 months, the insurance company needs to pay $500 million as the insurance compensation if the satellite stops functioning before 78 months. What is the probability that the insurance company needs to pay the insurance compensation?
2. If the insurance company charges $90 million for 78 months of insurance, how much profit does the insurance company expect to make (i.e., the expected value of the profit the insurance company will make)?
3. For how many months should the satellite be insured to be 98% confident that it will last beyond the insurance date?