Question 223170
A light bulb manufacturer claims his light bulbs will last 500 hours on the average. The lifetime of a light bulb is assumed to follow an exponential distribution.
a.	What is the probability that the light bulb will have to replaced within 500 hours?
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lamda = 1/500
Ans: P(x<=500) = 1 - e^(-lamda*x) = 1-e^[(-1/500)*500] = 1-e^-1 = 0.6321

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b.	What is the probability that the light bulb will last more than 1000 hours?
Ans:P(x>=1000) =  1 - P(x<=1000) = 1 -[1-e^(-1/500*1000)
= 1 -[1-e^(-2)] = e^(-2) = 0.1353
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c.	What is the probability that the light bulb will last between 200 and 800 hours?
Answer will be P(x<=800)-P(x<=200)
Remember P(x<=k) = 1-e^(-lambda*k)
I'll leave that to you.
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Cheers,
Stan H.