Why does the CLT matter?

Explain the **Central Limit Theorem (CLT)** and why it matters in data science and machine learning interviews. Then show how you would use the CLT to build a 95% confidence interval for an estimated metric such as: - average fraud loss per transaction, - average model score, or - average conversion rate in an experiment. Your answer should include: - the intuition behind the theorem - the mathematical statement at a high level - how the CLT justifies approximate inference for sample means - a small numeric example - when the approximation can fail or become unreliable, especially with heavy tails, dependence, clustering, very small samples, or rare-event data