Applying a limit theorem to approx. a probability

Question

Let $p=0.1$ the probability that a delivered apple is rotten.

Suppose someone orders $1000$ apples. How can I apply a limit theorem to approximately determine the probability that, for instance, at most 80 apples are rotten from the order?

Answer 1

The number of rotten apples follows a binomial distribution with $n=1000$ trials and probability of "success" $p=0.1$. If $X \sim \text{Binomial}(n,p)$ then you want $P(X \le 80)$. You have probably learned that for large $n$, the binomial distribution can be approximated by another distribution. Can you figure out which distribution (specifically, you not only need to identify the name/family, but also its parameters like mean and variance...) and finish from here?