| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Topic | Poisson distribution |
| Type | Three or more independent Poisson sums |
| Difficulty | Standard +0.3 Part (a) requires knowing that sum of independent Poissons is Poisson, then applying normal approximation with continuity correction—standard Further Stats technique. Part (b) is straightforward conceptual recall about Poisson assumptions (randomness/independence). Routine application of well-practiced methods with no novel insight required. |
| Spec | 5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.02n Sum of Poisson variables: is Poisson |
The average numbers of cars, lorries and buses passing a point on a busy road in a period of 30 minutes are 400, 80 and 17 respectively.
\begin{enumerate}[label=(\alph*)]
\item Assuming that the numbers of each type of vehicle passing the point in a period of 30 minutes have independent Poisson distributions, calculate the probability that the total number of vehicles passing the point in a randomly chosen period of 30 minutes is at least 520. [3]
\item Buses are known to run in approximate accordance with a fixed timetable.
Explain why this casts doubt on the use of a Poisson distribution to model the number of buses passing the point in a fixed time interval. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2021 Q2 [4]}}