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?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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