Suppose i have a continuos density function for a random variable x as such( function describes runtime for a program in seconds if it means anything):
$$ f(x) = \begin{cases} \left(\frac{3}{64}\right)x^2(4-x) & \text{for } 0 < x < 4 \\\ 0 & \text{otherwise}. \end{cases} $$
First I needed to find the probability for $p( x < 2)$ which is $0.3125$.
Now I'm asked, if you run the program 40 times, what is the probability that the average runtime for these 40 times is smaller than 2. I tried using the central limit theorem but i cant seem to get to the correct answer (which is $0.0008$). so help with finding an approach would help a lot.