Is it possible to apply the Central Limit Theorem to a population with a non-normal distribution?

Yes, the Central Limit Theorem (CLT) can be applied even if the population has a non-normal distribution. The CLT states that as the sample size becomes sufficiently large, the distribution of the sample mean will tend to be normal, regardless of the shape of the original distribution.

This means that as the sample size increases, the sum or average of independent random variables with the same distribution (even if non-normal) will approach a normal distribution.

However, it is important to consider:

• The sample size should be sufficiently large (usually n > 30 is considered enough, but it depends on the specific distribution).
• If the distribution is heavily skewed or has heavy tails, a larger sample may be required.

Thus, the CLT allows for the use of normal approximations for statistical inference even when the original data distribution is non-normal.