Math Statistics complicated question.. help..?

The lifetime of HP laptops is known to have an exponential distribution with an average of 40 months. You just bought an HP laptop.





a) find the probability that the laptop fails within the standards warranty period of 1 year?








b) Most people replace their laptop after 3 years of using and you are not an exception. Find the probability that the laptop is still working after 3 years of using?





c) If HP wants no more than 5% of their laptops to fail during the warranty period, how long should they change the standard warranty period to be?





ohhhhhh, I can't understand those :(

Math Statistics complicated question.. help..?
http://en.wikipedia.org/wiki/Exponential...





f(x) = λ e^(-λx)


x = number of years before laptop fails





since 1/λ = mean


we also know that average = 40 months = 40/12 years


λ = 3/10


.. . .


to answer a.


find P(X%26lt;1) = ∫(0 to 1) f(x) dx


....


b. = 1 - P(X %26lt; 3)


.. . .. .


c. you are looking for w such that P(X %26lt; w) = 1 - 0.05





you need GDC calculators for these otherwise...

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