| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | E(X) and Var(X) with probability calculations |
| Difficulty | Easy -1.2 This is a straightforward binomial distribution question requiring only direct application of standard formulas. Students need to recognize X ~ B(8, 0.2), then calculate P(X=3) using the binomial probability formula, find P(X≥3) = 1 - P(X≤2), and recall E(X) = np = 1.6. All three parts are routine textbook exercises with no problem-solving or conceptual challenges beyond basic recognition and formula application. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.02d Binomial: mean np and variance np(1-p) |
20% of packets of a certain kind of cereal contain a free gift. Jane buys one packet a week for 8 weeks. The number of free gifts that Jane receives is denoted by $X$. Assuming that Jane's 8 packets can be regarded as a random sample, find
\begin{enumerate}[label=(\roman*)]
\item P($X = 3$), [3]
\item P($X \geqslant 3$), [2]
\item E($X$). [2]
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2009 Q1 [7]}}