Question 419171: Manufacturer reliability ratings indicate that 9% of flux capacitors will fail at their scheduled lifetime of 2 years.
a.Given a random sample of 10 2-year-old flux capacitors, what is the probability
that 3 will have failed?
b.Suppose you do find that 3 have failed. What inference do you make?
This is the question as is. Please do not solve it for me, as I want to know how to do it.
My thoughts are:
That this is a exponential distribution problem (more specifically a survival).
I have equations for Length of life, and reliability, but I am having trouble figuring out where the information I am given goes into it.
So far I was thinking that Lambda = 2 years (nominal fail)
but that the problem is asking me directly fail rate AT the two year point does that mean the location factor is 2? (positive for shifting forward in time)
But I am not sure in this case if the sample size should have anything to do with the problem. (my initial thought is no)
I understand that part b is relating the output of part a with the 9% reliability rate, and probably wanting to know if an exponential model is the correct model. (If I am way off on thought, please tell me)
Thank you much for your time!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Manufacturer reliability ratings indicate that 9% of flux capacitors will fail at their scheduled lifetime of 2 years.
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a.Given a random sample of 10 2-year-old flux capacitors, what is the probability that 3 will have failed?
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Binomial Problem with n = 10 and p = 0.09
P(x = 3) = (0.09)^3
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b.Suppose you do find that 3 have failed.
What inference do you make?
Answer for yourself: Is that probability exceptional or
to be expected.
Cheers,
Stan H.
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