I am currently doing the following question from my textbook:
Let $W_1$, $W2$,.. be i.i.d. with distribution Exponential(3). Prove that for some $n$, we have $P(W_1 + W_2 +···+ W_n < n/2) > 0.999$
This appears to be a fairly basic application of the weak law of large numbers. I used $P(W_1 +\cdots+ W_n < n/2) = 1 − P(W_1 +\cdots+ W_n ≥ n/2)$. At this point I assume that I need to apply the weak law of large numbers but I'm unsure on how to go about that. Could someone point me in the right direction?