Central Limit Theorem
The Central Limit Theorem states that if X₁, X₂, ..., Xₙ are independent random variables from any distribution with mean μ and variance σ², then for large n, the sample mean x̄ is approximately normally distributed with mean μ and variance σ²/n. This holds regardless of the underlying distribution's shape.
Real World
Amazon's delivery-time data is right-skewed, yet when analysts average delivery times across 50 orders per warehouse, those averages follow an approximately normal distribution — enabling reliable performance benchmarks.
Exam Focus
State the conditions explicitly: independent observations, finite variance, and sufficiently large n (typically n ≥ 30).
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