| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Multiple independent time periods |
| Difficulty | Moderate -0.8 This is a straightforward application of the Poisson distribution formula with clearly stated parameters. Part (a) is pure substitution into P(X=0), part (b) requires recognizing the rate scales to λ=5.4 for 6 months, and part (c) combines Poisson with binomial reasoning. All steps are standard textbook exercises with no novel insight required, making this 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 |
On a stretch of motorway accidents occur at a rate of 0.9 per month.
\begin{enumerate}[label=(\alph*)]
\item Show that the probability of no accidents in the next month is 0.407, to 3 significant figures. [1]
Find the probability of
\item exactly 2 accidents in the next 6 month period, [3]
\item no accidents in exactly 2 of the next 4 months. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q2 [7]}}