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      Question

      The 'Central Limit Theorem' (CLT) states

      that:
      A all datasets follow a normal distribution if large enough Correct Answer Incorrect Answer
      B the sampling distribution of the sample mean approaches a normal distribution as sample size increases Correct Answer Incorrect Answer
      C the mean of any dataset equals the median for symmetric distributions Correct Answer Incorrect Answer
      D statistical models become more accurate as dataset size increases Correct Answer Incorrect Answer
      E the number of features that can be used in a statistical model is limited Correct Answer Incorrect Answer

      Solution

      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.

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