| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2009 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Approximating the Binomial to the Poisson distribution |
| Type | Calculate single probability using Poisson approximation |
| Difficulty | Standard +0.3 This is a straightforward application of Poisson approximation to binomial with standard parameter calculation (λ = np) and cumulative probability lookup. Part (a) requires P(X ≥ 4) = 1 - P(X ≤ 3) with λ = 6, and part (b) uses λ = 24 with P(X ≤ 20). Both parts are routine S2 bookwork with no conceptual challenges beyond recognizing the Poisson model and using tables correctly. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.04b Linear combinations: of normal distributions5.05a Sample mean distribution: central limit theorem |
\begin{enumerate}
\item An administrator makes errors in her typing randomly at a rate of 3 errors every 1000 words.\\
(a) In a document of 2000 words find the probability that the administrator makes 4 or more errors.
\end{enumerate}
The administrator is given an 8000 word report to type and she is told that the report will only be accepted if there are 20 or fewer errors.\\
(b) Use a suitable approximation to calculate the probability that the report is accepted.
\hfill \mbox{\textit{Edexcel S2 2009 Q5 [10]}}