A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 90 months and a standard deviation of 3.7 months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for $50 million. Assume that the only part of the satellite in question is the microchip; all other components will work indefinitely.
(a) For how many months should the satellite be insured to be 99% confident that it will last beyond the insurance date?
(b) If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends?
(c) If the satellite is insured for 84 months, what is the expected loss to the insurance company?
(d) If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make?