Question

If the random variable X follows a distribution that is known not to be normal, how many observations must be included in a sample for us to be able to safely assume that the sample mean follows a normal distribution?

Answer 1

According to the central limit theorem given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

The more observations you add to a sample distribution from the population distribution, the more it looks like the population distribution.

To safely assume that the sample mean follows a normal distribution 30 observations must be included in a sample.