| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Probability of range of values |
| Difficulty | Moderate -0.8 This is a straightforward application of binomial distribution with standard cumulative probability calculations. Students need only to recognize the binomial setup (fixed n, constant p) and use tables or calculator for P(U≤5), P(U≥3)=1-P(U≤2), and P(V=4). No problem-solving insight required, just routine procedure—easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
5 (i) $20 \%$ of people in the large town of Carnley support the Residents' Party. 12 people from Carnley are selected at random. Out of these 12 people, the number who support the Residents' Party is denoted by $U$.
Find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { P } ( U \leqslant 5 )$,
\item $\quad \mathrm { P } ( U \geqslant 3 )$.\\
(ii) $30 \%$ of people in Carnley support the Commerce Party. 15 people from Carnley are selected at random. Out of these 15 people, the number who support the Commerce Party is denoted by $V$.
Find $\mathrm { P } ( V = 4 )$.
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2008 Q5 [8]}}