# How do you solve for lambda in an exponential distribution?

I am working on a problem and am unsure how to solve it.

The problem: Find an exponential distribution such that P(Z $$\ge$$ 3) = .04

What I have done so far:

P(Z$$\ge$$3) = 1 - P(Z$$\lt$$ 3)

We are solving for $$\lambda$$ in X ~ Exp($$\lambda$$)

Quantile is 4% (I think)

What steps do I need to do to solve this problem?

\begin{align} \mathbb{P}(Z \geq 3) = \int_3^{\infty} \lambda e^{-\lambda x} dx = [-e^{-\lambda x}]_3^{\infty} = e^{-3\lambda}, \end{align}
hence $$\mathbb{P}(Z \geq 3) = 0.04$$ iff $$\lambda = \frac{\log(0.04)}{-3}$$.