based on my question I aksed yesterday, (look at the accepted answer) 2500 people have a car insurance there are 1500 women and 1000 men. Estimate probability that in the next year there will be at least 25 car accidents
I have a small question about Lyapunov CLT, doing another exercise involving this theorem I've noticed that I've obtained a better final result approximation than the approximation I'd obtain using central limit theorem as it is, because when I have to use gaussian tables, I've noticed that the result is 0.65542, and not 0.715 (0.715 is the textbook result). I was wondering if it's just a random lucky guess, or if there's a way to formalize this raw idea in an intuitive way, because I actually don't have enough stats knowledge to understand difficult explanations.
my idea is that Lyapunov theorem round the number better than central limit theorem. If it's true, then it'd makes sense to use Lyapunov theorem instead of CLT.