##### Scenario Assessing statistical knowledge for disease-testing model evaluation ##### Question Explain the Central Limit Theorem, its prerequisites, and when it fails. Describe Bayesian inference and why it is widely used. A disease affects 1/1000 people. A test predicts positives with 95% accuracy and negatives with 98% accuracy. If the test flags someone positive, what’s the probability they are truly infected? Show your reasoning. ##### Hints Discuss i.i.d. assumptions, sampling size, Bayes’ formula; build a confusion matrix and compute posterior probability.