My Notes Ask Your Teach 8.14 points Pievous Answers BBUnderStat1263035 A relay m

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My Notes Ask Your Teach 8.14 points Pievous Answers BBUnderStat1263035 A relay microchip in a telecommunications satelite has a life expectancy that follows a normal distribution with a mean of 93 months London insurance company is going to insure the satellite for S0 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 93% confident that it will last beyond the insurance date? (Round your answer to the nearest month.) months (b) If the satelite 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) 00075 (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) 0.0075 (d) If the insurance company charges $3 million for B4 months of Insurance, how much profit does the company expect to make? (Round your answer to the nearest dollar) 2 9925 Need Help? L SubmitAnswerIisave Progre ILPracticeAr other Version] Submit Assignment Save Assignment Progress Home My Assignmants Extension Request

Explanation / Answer

Solution:

a) = 93 months
= 3.7 months
P(x < a) = 0.93
P(x - < a- ) = 0.93
P(x - / < a- /) = 0.93
But x - / = z
P(z < a-93/3.7) = 0.93
a-93/3.7 = 1.4758 => Use the Excel formula "= NORMSINV(0.93)"
a = 93+ 1.4758 * 3.7 = 99 months

b) = 93 months
= 3.7 months
P(x < 84) = P(x- < a- ) = P(x- / < a-/)
But x-/ = z
P(x < 84) = P(z < 84- 93/3.7) = P(z < -2.4324) = 0.0075

c) Expected Loss = P(x < 84) * 50 million dollars
= 0.0075 * 50 million dollars
= $375000
d) Expected Profit = $3 million - $375000 = $2625000

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