| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Single time period probability |
| Difficulty | Easy -1.2 This is a straightforward recall and calculation question requiring only direct application of standard distribution formulas or tables. Part (a) involves summing Poisson probabilities P(X=0) through P(X=3) using the given mean, while part (b) requires looking up or calculating a cumulative binomial probability. No problem-solving, interpretation, or conceptual understanding beyond basic definitions is needed—purely mechanical computation typical of early S2 exercises. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
| Answer | Marks |
|---|---|
| \(e^{-1.4}(1 + 1.4 + \frac{1.4^2}{1!} + \frac{1.4^3}{3!})\) | M1 A1 |
| \(= 0.9463\) (4sf) | A1 |
| Let \(A \sim B(20, 0.4)\) | M1 |
| \(P(Y \leq 12) = P(A \geq 8)\) | M1 |
| \(= 1 - P(A \leq 7)\) | M1 |
| \(= 1 - 0.4159 = 0.5841\) | A1 |
$e^{-1.4}(1 + 1.4 + \frac{1.4^2}{1!} + \frac{1.4^3}{3!})$ | M1 A1 |
$= 0.9463$ (4sf) | A1 |
Let $A \sim B(20, 0.4)$ | M1 |
$P(Y \leq 12) = P(A \geq 8)$ | M1 |
$= 1 - P(A \leq 7)$ | M1 |
$= 1 - 0.4159 = 0.5841$ | A1 |
---\begin{enumerate}
\item (a) The random variable $X$ follows a Poisson distribution with a mean of 1.4
\end{enumerate}
Find $\mathrm { P } ( X \leq 3 )$.\\
(b) The random variable $Y$ follows a binomial distribution such that $Y \sim \mathrm {~B} ( 20,0.6 )$.
Find $\mathrm { P } ( Y \leq 12 )$.\\
(4 marks)\\
\hfill \mbox{\textit{Edexcel S2 Q1 [7]}}