| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Compare approximation methods |
| Difficulty | Standard +0.3 This is a standard S2 approximation question requiring routine application of continuity corrections and distribution approximations. While it involves multiple parts and comparing methods, the techniques are textbook procedures with no novel problem-solving required. The Poisson approximation is slightly unusual (Normal is more appropriate here), but the calculations themselves are straightforward, making this slightly easier than average. |
| Spec | 2.04c Calculate binomial probabilities2.04d Normal approximation to binomial2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
6. The probability that a sunflower plant grows over 1.5 metres high is 0.25 . A random sample of 40 sunflower plants is taken and each sunflower plant is measured and its height recorded.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that the number of sunflower plants over 1.5 m high is between 8 and 13 (inclusive) using
\begin{enumerate}[label=(\roman*)]
\item a Poisson approximation,
\item a Normal approximation.
\end{enumerate}\item Write down which of the approximations used in part (a) is the most accurate estimate of the probability. You must give a reason for your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2008 Q6 [12]}}