| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating the Poisson to the Normal distribution |
| Type | Justify use of normal approximation |
| Difficulty | Moderate -0.5 This is a straightforward application of the normal approximation to the Poisson distribution. Students need to justify λ=20 is large enough (standard criterion λ>15), apply continuity correction, standardize to find P(D≥24.5), and use normal tables. While it requires multiple steps, each is routine and follows a standard procedure taught explicitly in S2. |
| Spec | 2.04d Normal approximation to binomial5.02i Poisson distribution: random events model |
2 The random variable $D$ has the distribution $\operatorname { Po } ( 20 )$. Using an appropriate approximation, which should be justified, calculate $\mathrm { P } ( D \geqslant 25 )$.
\hfill \mbox{\textit{OCR S2 2009 Q2 [6]}}