Let $X$ be a binomial random variable $X \sim Bi(p, t)$. ($t$ is the number of tosses)
Is there a way to estimate $$P(X \ge \alpha t + \beta)$$?
I know that I can write the probability exactly but it's not very useful as it's a sum which I'm not sure how to operate.
$t$ here is supposed to be finite, but even taking $t \to \infty$ doesn't really help because after normalizing the LHS goes to a normal but the RHS blows up
Have you any resource / advice?