Let $X_1,\cdots,X_{125}$ be i.i.d.random variables with binomial distribution with parameter $\left(8,\dfrac1{200}\right)$. We define a random variable $S$ as $$ S(\omega)=\sum_{i=1}^{125}X_i(\omega)$$ and$$ A=\min\{m\in\mathbb{N}:P(S\le m)\ge0.96\}. $$ I have to estimate $m$ using Chebyschev inequality.
I state that since $S$ is defined as a sum of binomial variables, so $S\sim Bin(8\cdot125, 1/200) $ so $E[S]=5$ and $Var(S)=199/40$. Now I know that Chebyschev inequality is used to find the number of values that can be more than a certain distance from the mean, but I don't know how to apply it to find $m$. Any ideas or hints?