SAMPLE SIZES AND THE CENTRAL-LIMIT-THEOREM - THE POISSON-DISTRIBUTIONAS AN ILLUSTRATION

Poisson distributions are often used to show that the central limit th eorem is valid even for discrete and for highly skewed distributions. It is not so commonly appreciated that they can also be used to demons trate that, in some cases, very large sample sizes may not be enough t o invoke the theorem. Binomial distributions can be used in a similar manner.