Math
Central limit theorem.
Definition
A fundamental theorem stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's original distribution. Generally, n ≥ 30 is considered sufficient for the approximation.
Examples
Real-world.
- 1 Even if individual die rolls are uniformly distributed, the average of 50 rolls will be approximately normally distributed
- 2 Quality control: the mean weight of samples of 40 cereal boxes will follow a normal distribution even if individual box weights are skewed
Key Fact
For large n: x̄ ~ N(μ, σ/√n) regardless of population shape