How to determine distribution and expected value?

Question

I am struggling with part ii) of the following question.

How do I determine the distribution of $s$?

Answer 1

Hint:

The domain of $s$ is given by $D=[0,3]$. Now for $x\in D$ we have $$ P(s\le x) = P(0.003p^2\le x) = P\left(p\le\sqrt{\frac{x}{0.003}}\right) $$