| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2013 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Explain or apply conditions in context |
| Difficulty | Standard +0.3 This is a straightforward application of the Poisson distribution requiring rate scaling (week to day, week to 28 days) and standard probability calculations using tables or calculator. Part (b) requires simple recall of Poisson conditions. The multi-part structure and time-scaling adds minor complexity above the most routine questions, but all techniques are standard S2 material with no problem-solving insight required. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.02l Poisson conditions: for modelling5.02m Poisson: mean = variance = lambda |
4 Gamma-ray bursts (GRBs) are pulses of gamma rays lasting a few seconds, which are produced by explosions in distant galaxies. They are detected by satellites in orbit around Earth. One particular satellite detects GRBs at a constant average rate of 3.5 per week (7 days).
You may assume that the detection of GRBs by this satellite may be modelled by a Poisson distribution.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that the satellite detects:
\begin{enumerate}[label=(\roman*)]
\item exactly 4 GRBs during one particular week;
\item at least 2 GRBs on one particular day;
\item more than 10 GRBs but fewer than 20 GRBs during the 28 days of February 2013.
\end{enumerate}\item Give one reason, apart from the constant average rate, why it is likely that the detection of GRBs by this satellite may be modelled by a Poisson distribution.\\
(1 mark)
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2013 Q4 [9]}}