Suppose Y ~ Poisson(100). Using the central limit theorem to estimate P(80 ≤ Y ≤ 120)
The answer is P (80−100)/10 ≤ X1+···+X100−100µ /√ 100 σ ≤ (120−100)/ 10.
I think since they assume that 100 is large enough to use the central limit theory, they used Z = (x - µ) / σ to standardize distribution. However, I learned that when you are dealing with sampling distribution and n is large enough, you use Z = (x - µ) / (σ /√n). So I was wondering if there is a way to know when to use which Z.
Thank you!