So, I have a sample size of $220$, and I'm trying to use normal approximation to calculate the minimum amount of times the outcome $A$ is expected to happen at $99$%. In other words, I'm interested in knowing the breakpoint where the likelihood for $A$ happening $x$ or less times is, at most, 1%.
Through the power of cheating I know that the correct answer is $40$, but I'm trying to understand how it's actually calculated. The 40 would mean "the minimum amount of times $A$ happens at 99% probability" or in other words "The probability Not $A$ happening ($220-40=180$) times is 1% or less"
Here's an example question if what I'm trying to calculate was confusing:
An airline that has 220 passengers traveling knows that 25% of the passengers never show up. They want to calculate how many seats the airplane they use for the flight has to have so that the likelihood of not having enough seats for the passengers that do show up is, at most, 1%.