Let $X_1,X_2,X_3,....,X_n \stackrel{i.i.d}{\sim}$ U($-0.5$,$0.5$) and let
T= $X_1+X_2+X_3+....+X_n$.
Suppose $n=100$, Then $P(T^2>25)$ is?
How do I solve such problem? I found out the sum of two and three i.i.d uniform random variables using convolution theorem, but it became more complicated after that. I know that this could be solved using property of i.i.d rv's but could not figure out how. Please help.