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# a relay microchip

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 3.3 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.) 98 l X 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.) 0.0008 x (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.)
\$ 400000 l x (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.) \$ 2576000 x

a. 94% confidence that it last beyond 87 months b. The probability that... View the full answer

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