Probability Distributions Used In Acceptance Sampling

In basic acceptance sampling techniques three most common distributions used are:
Hypergeometric: Parameters N, X, n
Binomial: Parameters n,p
Poisson: Parameter λ
Normal: Parameter µ, σ

Approximations

1. When N is large or n/N <0.1 then Hypergeometric (N, X, n) → Normal (n, X/N)
2. When n → ∞ and p → 0  such that np → λ (some constant) then Binomial (n, p) → Poisson(λ)
3. For large values of λ Poisson → Normal

A hypergeometric distribution has finite population, a binomial has infinite or very large population or the experiment is done on a finite population with replacement and a poisson has infinite chances of occurrences.

PS: Corrections/Additions/Suggestions are welcome.