| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2007 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Single time period probability |
| Difficulty | Moderate -0.8 This is a straightforward computational question requiring only direct application of standard distribution formulas from the formula booklet. Part (a) uses Poisson tables or calculator for a tail probability, and part (b) uses binomial probability formula for two simple cases. No problem-solving, interpretation, or conceptual understanding beyond basic recall is needed. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(J \geq 10) = 1 - P(J \leq 9)\) or \(= 1 - P(J < 10)\) | M1 | |
| \(= 1 - 0.9919\) | implies method | A1 (2 marks) |
| \(= 0.0081\) | awrt 0.0081 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(K \leq 1) = P(K = 0) + P(K = 1)\) both, implied below even with '25' missing | M1 | |
| clear attempt at '25' required | M1 | |
| \(= (0.73)^{25} + 25(0.73)^{24}(0.27)\) | M1 | |
| \(= 0.00392\) | awrt 0.0039 implies M | A1 (3 marks) |
**Part (a)**
$P(J \geq 10) = 1 - P(J \leq 9)$ or $= 1 - P(J < 10)$ | M1 |
$= 1 - 0.9919$ | implies method | A1 (2 marks) |
$= 0.0081$ | awrt 0.0081 | A1 |
**Part (b)**
$P(K \leq 1) = P(K = 0) + P(K = 1)$ both, implied below even with '25' missing | M1 |
clear attempt at '25' required | M1 |
$= (0.73)^{25} + 25(0.73)^{24}(0.27)$ | M1 |
$= 0.00392$ | awrt 0.0039 implies M | A1 (3 marks) |
---2. The random variable $J$ has a Poisson distribution with mean 4.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { P } ( J \geqslant 10 )$.
The random variable $K$ has a binomial distribution with parameters $n = 25 , p = 0.27$.
\item Find $\mathrm { P } ( K \leqslant 1 )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2007 Q2 [5]}}