| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating the Binomial to the Poisson distribution |
| Type | Combined independent Poisson probabilities |
| Difficulty | Standard +0.3 This is a straightforward two-part Poisson question requiring students to (i) combine Poisson distributions using the additive property, calculate P(X≥5), then use binomial distribution for 20 trials, and (ii) state independence. While it involves multiple steps and two distributions, each step follows standard S3 procedures with no novel insight required—slightly easier than average due to its routine nature. |
| Spec | 5.02i Poisson distribution: random events model5.02k Calculate Poisson probabilities5.02n Sum of Poisson variables: is Poisson |
2 The number of bacteria in 1 ml of drug $A$ has a Poisson distribution with mean 0.5. The number of the same bacteria in 1 ml of drug $B$ has a Poisson distribution with mean 0.75 . A mixture of these drugs used to treat a particular disease consists of 1.4 ml of drug $A$ and 1.2 ml of drug $B$. Bacteria in the drugs will cause infection in a patient if 5 or more bacteria are injected.\\
(i) Calculate the probability that, in a sample of 20 patients treated with the mixture, infection will occur in no more than one patient.\\
(ii) State an assumption required for the validity of the calculation.
\hfill \mbox{\textit{OCR S3 2009 Q2 [8]}}