A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with mean μ= 90 months and a standard deviation σ= 3.7 months. When this computer relay...

A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with mean μ= 90 months and a standard deviation σ= 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 dollars. Assum that the only part of the satellite in question us the microchip. All other components will work indefinitely.

A.) for how many months should the satellite be insures for to be 95% secure that it will last beyond the insurance date?

B.) if the satellite is insured for 80 months, what is the probability that it will malfunction before the coverage expires?