The 'Central Limit Theorem' (CL

CLT states that given a population with mean μ and standard deviation σ, the distribution of sample means (x̄) from samples of size n approaches N(μ, σ/√n) as n → ∞ (typically n ≥ 30 is sufficient). This is foundational because it justifies using normal distribution assumptions for hypothesis testing even when the population isn't normal, enables construction of confidence intervals, and underlies most parametric statistical tests (t-tests, ANOVA). In banking it allows estimating population-level credit risk from sample data and enables sampling-based audit procedures.