| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2009 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Single time period probability |
| Difficulty | Moderate -0.3 This is a straightforward application of standard Poisson distribution techniques: parts (i) and (ii) involve direct substitution into the Poisson formula and using the scaling property (λ scales with time), while part (iii) requires only qualitative understanding of Poisson distribution shape. All parts are routine S2 exercises with no problem-solving insight 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 |
3 The number of incidents of radio interference per hour experienced by a certain listener is modelled by a random variable with distribution $\operatorname { Po } ( 0.42 )$.\\
(i) Find the probability that the number of incidents of interference in one randomly chosen hour is
\begin{enumerate}[label=(\alph*)]
\item 0 ,
\item exactly 1 .\\
(ii) Find the probability that the number of incidents in a randomly chosen 5-hour period is greater than 3.\\
(iii) One hundred hours of listening are monitored and the numbers of 1 -hour periods in which 0,1 , $2 , \ldots$ incidents of interference are experienced are noted. A bar chart is drawn to represent the results. Without any further calculations, sketch the shape that you would expect for the bar chart. (There is no need to use an exact numerical scale on the frequency axis.)
\end{enumerate}
\hfill \mbox{\textit{OCR S2 2009 Q3 [8]}}