A factory manufactures a product with a life cycle that follows the exponential distribution. Specify the parameter λ when it is known that 80% of the products last at least 3 years.
And the answer is $=\frac{-ln(4/5)}{3} ≈ 0.07$.
I ran into this question while browsing the new textbook and I'm curious how they came up with that answer.
The pdf for the exponential distribution is $\lambda\cdot e^{-\lambda x}$ for $x\ge 0$ (and $0$ elsewhere).
So your information works out to $\int_3^\infty \lambda\cdot e^{-\lambda x} dx=0.80$.
From here you can work out the integral and solve the resulting equation for $\lambda$.