| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2009 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Finding maximum n for P(X=0) threshold |
| Difficulty | Standard +0.3 This is a straightforward multi-part Poisson distribution question requiring standard applications: calculating probabilities with given λ, solving e^(-λx) = 0.80 for x (which simplifies to taking natural logs), and computing expected value using probabilities. All techniques are routine S2 material with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
8. A cloth manufacturer knows that faults occur randomly in the production process at a rate of 2 every 15 metres.
\begin{enumerate}[label=(\alph*)]
\item Find the probability of exactly 4 faults in a 15 metre length of cloth.
\item Find the probability of more than 10 faults in 60 metres of cloth.
A retailer buys a large amount of this cloth and sells it in pieces of length $x$ metres. He chooses $x$ so that the probability of no faults in a piece is 0.80
\item Write down an equation for $x$ and show that $x = 1.7$ to 2 significant figures.
The retailer sells 1200 of these pieces of cloth. He makes a profit of 60p on each piece of cloth that does not contain a fault but a loss of $\pounds 1.50$ on any pieces that do contain faults.
\item Find the retailer's expected profit.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2009 Q8 [13]}}