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 3.8 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 96% confident that it will last beyond the insurance date?

Question

Mathematics

Jazmine Hayden

11 September, 17:18

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 3.8 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 96% confident that it will last beyond the insurance date?

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Answers (1)

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Damion Pace · Answer 1

The insurance period must be chosen so that the probability of a microchip failure within that period is 4%. Reference to a standard normal distribution table shows that the z-score for a cumulative probability of 4% is - 1.75.

Let the insurance period be X months:

-1.75 = (X - 93) / 3.8

-6.65 = X - 93

X = 83.35 months.

The answer is 83.35 months.