# relationship between the probability of sum of iid random variable and the probability of one random variable

I have $n$ iid random variables $X_i$, which satisfy $X_i>0$. I want to know the relationship between the following two probabilities, $$\mathbb{P}\left(\sum_{i=1}^{n}X_i > z \right) \qquad \text{ and } \qquad \mathbb{P}\left(X_i > z\right)$$ Or equivalently, how to approximate $\mathbb{P}\left(\sum_{i=1}^{n}X_i > z \right)$ using $\mathbb{P}(X_i > z )$ as tight as possible?