| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Poisson with binomial combination |
| Difficulty | Standard +0.3 This is a straightforward application of Poisson distribution with standard scaling of the parameter. Part (a) is direct formula substitution, part (b) requires binomial probability with Poisson components but follows a standard pattern, and part (c) involves routine normal approximation to Poisson. All techniques are standard S2 content with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04d Normal approximation to binomial5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
From past records, a manufacturer of twine knows that faults occur in the twine at random and at a rate of 1.5 per 25 m.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that in a randomly chosen 25 m length of twine there will be exactly 4 faults. [2]
\end{enumerate}
The twine is usually sold in balls of length 100 m. A customer buys three balls of twine.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the probability that only one of them will have fewer than 6 faults. [6]
\end{enumerate}
As a special order a ball of twine containing 500 m is produced.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Using a suitable approximation, find the probability that it will contain between 23 and 33 faults inclusive. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q6 [14]}}