| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| 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 sampling distribution theory with a normal population. Part (a) requires direct recall of the formula for the distribution of the sample mean (mean μ, standard deviation σ/√n). Part (b) is a routine probability calculation using standardization. No problem-solving insight required, just mechanical application of standard formulas. |
| Spec | 5.05a Sample mean distribution: central limit theorem5.05d Confidence intervals: using normal distribution |
A random sample $X_1, X_2, \ldots, X_{10}$ is taken from a normal population with mean 100 and standard deviation 14.
\begin{enumerate}[label=(\alph*)]
\item Write down the distribution of $\overline{X}$, the mean of this sample. [2]
\item Find $\text{Pr}(|\overline{X} - 100| > 5)$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 Q1 [5]}}