| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Random sampling methodology |
| Difficulty | Moderate -0.8 This is a straightforward probability question requiring only basic binomial probability calculation (or direct multiplication) and interpretation. Part (i) is routine: P(X≤500) = (500/600)^12, a simple one-step calculation. Part (ii) requires only a brief comment that the result, while unlikely, doesn't prove bias. No complex reasoning, proof, or multi-step problem-solving is needed—this is easier than a typical A-level question. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.04c Calculate binomial probabilities |
2 A village has a population of 600 people. A sample of 12 people is obtained as follows. A list of all 600 people is obtained and a three-digit number, between 001 and 600 inclusive, is allocated to each name in alphabetical order. Twelve three-digit random numbers, between 001 and 600 inclusive, are obtained and the people whose names correspond to those numbers are chosen.\\
(i) Find the probability that all 12 of the numbers chosen are 500 or less.\\
(ii) When the selection has been made, it is found that all of the numbers chosen are 500 or less. One of the people in the village says, "The sampling method must have been biased." Comment on this statement.
\hfill \mbox{\textit{OCR S2 2008 Q2 [5]}}