Let $X_i$ be independent and identically distributed exponential with $\lambda = 2$ for $i = 1,\dotsc,10$. Estimate the probability $P(X_1 +···+ X_{10} > 3)$.
I tried to use the independent properties var$(x+y)=$ var$(x)+$var$(y)$ they are independent to find the mean is $0.5\cdot 10$ and the variance is $0.25\cdot 10$ so I am finding the $P(z>\frac{3-5}{\sqrt{2.5}})$ am I correct or the question is asking for something else?