| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Finding minimum stock level for demand |
| Difficulty | Moderate -0.3 This is a straightforward application of Poisson distribution with λ=1.5. Parts (a) and (b) involve direct probability calculations using P(X=0) and P(X>5). Part (c) requires finding the minimum value by cumulative probability, which is routine for S2 level. All parts are standard textbook exercises 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 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(X \sim \text{Po}(1.5)\); From tables, \(P(X = 0) = 0.223\) | B1 | |
| (b) \(P(X > 5) = 1 - 0.9955 = 0.0045\) | M1 A1 | |
| (c) \(P(X \leq 3) = 0.9344\) and \(P(X \leq 4) = 0.9814\), so he needs 4 copies | M1 M1 A1 | Total: 6 marks |
(a) $X \sim \text{Po}(1.5)$; From tables, $P(X = 0) = 0.223$ | B1 |
(b) $P(X > 5) = 1 - 0.9955 = 0.0045$ | M1 A1 |
(c) $P(X \leq 3) = 0.9344$ and $P(X \leq 4) = 0.9814$, so he needs 4 copies | M1 M1 A1 | Total: 6 marks2. The number of copies of The Statistician that a newsagent sells each week is modelled by a Poisson distribution. On average, he sells 1.5 copies per week.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that he sells no copies in a particular week.
\item If he stocks 5 copies each week, find the probability he will not have enough copies to meet that week's demand.
\item Find the minimum number of copies that he should stock in order to have at least a $95 \%$ probability of being able to satisfy the week's demand.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q2 [6]}}