The central limit theorem applies to sample means taken from:

1. The theorem's power lies in how few assumptions it needs. 2. The law of large numbers applies if you take samples of larger and larger size from any population. 3. As sample sizes increase, the distribution of means more closely follows the normal distribution. 4. A far-from-normal population simply needs more observations before the effect shows. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 7 'The Central Limit Theorem', sections 7.1-7.3_