Let $X$= amount of insurance reimbursement for dental expense. The pdf of $X$ is $F(x) = ce^{-.004x} \text{ for } x>0$.
a) Find c. Hint: You can do this several ways. One way is to notice that X is an exponential RV.
For this question I am aware of two things. One is that for an exponential distribution $g(x, \theta) = 1/e^{-x/\theta}$ for $x>0$. I also know that the integral for any pdf of the function equals $1$.
I'm just unsure how to combine this information to find $c$.
Part b asks to calculate the $80$th percentile. [Hint: The $r$th percentile is the $x$-value, say $x=R$, for which the areas under $f$ to the left of $x=R$ is equal to $r$ percent.]