Question

In statistics, is there a golden rule or a procedure that can be applied given a problem that will help me I identify when I should apply the central limit theorem vs. applying e.g. binomial probability or sample size estimate.

Answer 1

The central limit theorem is used for inferences about a mean. The central limit theorem says that the mean of a large sample from a distribution with finite variance has an approximate normal distribution. The size of the sample before we regard the approximation is good enough depends on the distribution, but without outliers, we can use the sample mean as an estimate of the population mean and find the error probabilities.

This is applicable where we expect the data to come from normal distribution which looks like

The binomial distribution gives the discrete probability distribution of obtaining exactly successes out of Bernoulli trials (where the result of each Bernoulli trial is true with probability and false with probability ).

Binomials are usually in the form of binary variables such as yes, no true.false questions