S3 June 2011 Q1
1. Explain what you understand by the Central Limit Theorem. (3)
| Scheme | Marks |
|---|---|
| \(X_1, X_2, \ldots X_n\) is a random sample of size \(n\), for large \(n\), | B1 |
| drawn from a population of any distribution with mean \(\mu\) and variance \(\sigma^2\) | B1 |
| then \(\overline{X}\) is (approximately) \(\mathrm{N}\left(\mu, \dfrac{\sigma^2}{n}\right)\) | B1 |
| (3) | |
| (3 marks) |
Notes
1st B for large sample or equivalent
2nd B for ‘population of any distribution’ or ‘any population’
3rd B require mean or symbol and normal ( parameters not required)