| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | State distribution of sample mean |
| Difficulty | Moderate -0.8 This is a straightforward application of the central limit theorem requiring students to state the sampling distribution of the mean (with standard error σ/√n) and then perform a routine normal probability calculation. Both parts are direct recall and standard procedure with no problem-solving or conceptual challenges. |
| Spec | 5.05a Sample mean distribution: central limit theorem |
The weights of pears, $P$ grams, are normally distributed with a mean of 110 and a standard deviation of 8. Geoff buys a bag of 16 pears.
\begin{enumerate}[label=(\alph*)]
\item Write down the distribution of $\overline{P}$, the mean weight of the 16 pears. [2]
\item Find P$(110 < \overline{P} < 113)$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 Q2 [5]}}