SOLUTION: 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
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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?
b. What is the probability that the light bulb will last more than 1000 hours?
c. What is the probability that the light bulb will last between 200 and 800 hours?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
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