| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Single batch expected count |
| Difficulty | Moderate -0.8 This is a straightforward application of the binomial distribution formula for part (i), followed by a simple expected value calculation (multiplying probability by 100) for part (ii). Both parts require only direct recall of standard formulas with no problem-solving or conceptual challenges. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
1 In a multiple-choice test there are 30 questions. For each question, there is a $60 \%$ chance that a randomly selected student answers correctly, independently of all other questions.\\
(i) Find the probability that a randomly selected student gets a total of exactly 20 questions correct.\\
(ii) If 100 randomly selected students take the test, find the expected number of students who get exactly 20 questions correct.
\hfill \mbox{\textit{OCR MEI S1 Q1 [5]}}