Probability Density Function Help

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Probability Density Function...Help

The probabiltiy density function of the time to failure of an electric component in hours is f(x)=e^{(-x/3000)/3000} for x > 0 and f(x) = 0 for x \leq 0 determine the probability that

a) A component last more than 1000 hours before failure
I know how to solve this part. All I have to to is integrate the given function from [1000, infinity].

But how do determine the number of hours at which 10% of all the components have failed? I don't know what interval I should integrate over. Any Ideas?
 
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If F(x) is the probability that a component has failed by time x, you are looking for when F(x) = .10. Can you solve that?
 
yes I can. thank you!
 
when I solve it as you state that is no the answer.
any other ideas?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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