A relay microchip in a telecommunications satellite has a life expectancy that f

Question

A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3.2 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 94% confident that it will last beyond the insurance date? (Round your answer to the nearest month.) months

(b) If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends? (Round your answer to four decimal places.)

(c) If the satellite is insured for 84 months, what is the expected loss to the insurance company? (Round your answer to the nearest dollar.) $ (d) If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make? (Round your answer to the nearest dollar.)

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 92
standard Deviation ( sd )= 3.2
a.
P ( Z < x ) = 0.94
Value of z to the cumulative probability of 0.94 from normal table is 1.554774
P( x-u/s.d < x - 92/3.2 ) = 0.94
That is, ( x - 92/3.2 ) = 1.554774
--> x = 1.554774 * 3.2 + 92 = 96.975276
b.
P(X < 84) = (84-92)/3.2
= -8/3.2= -2.5
= P ( Z <-2.5) From Standard Normal Table
= 0.0062
c.
the product of 50 million and the probability you find in b is ultimately the expected loss
0.0062*50 Million = 0.31 million loss
d.
It's 3 million in revenue minus the- expecetd loss = 3 million- 0.31 million loss = 2.69 profit

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