Question

A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 93 months and a standard deviation of 3.0 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. 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? (Round your answer to the nearest month.)

Answer 1

Solution:-

Given that,

mean = = 93

standard deviation = = 3.0

Using standard normal table,

P(Z > z) = 99%

= 1 - P(Z < z) = 0.99  

= P(Z < z) = 1 - 0.99

= P(Z < z ) = 0.01

= P(Z < -2.326 ) = 0.01  

z = -2.326

Using z-score formula,

x = z * +

x = -2.326 * 3.0 + 93

x = 86 months