| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2009 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Approximating the Binomial to the Poisson distribution |
| Type | Calculate single probability using Poisson approximation |
| Difficulty | Standard +0.3 This is a straightforward application of the Poisson approximation to the binomial distribution with clear parameters (n=60, p=0.15, λ=9). Part (b) requires recognizing when to use the approximation and computing P(X<13) from tables or calculator, which is standard S2 material but slightly above average difficulty due to the two-sample setup requiring students to combine samples correctly. |
| 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)5.02n Sum of Poisson variables: is Poisson |
\begin{enumerate}
\item A bag contains a large number of counters of which $15 \%$ are coloured red. A random sample of 30 counters is selected and the number of red counters is recorded.\\
(a) Find the probability of no more than 6 red counters in this sample.
\end{enumerate}
A second random sample of 30 counters is selected and the number of red counters is recorded.\\
(b) Using a Poisson approximation, estimate the probability that the total number of red counters in the combined sample of size 60 is less than 13.\\
\hfill \mbox{\textit{Edexcel S2 2009 Q1 [5]}}