| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2010 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Known variance confidence intervals |
| Difficulty | Moderate -0.3 This is a straightforward application of normal distribution and CLT with known variance. Part (a) is basic normal probability, part (b) applies standard error formula (σ/√n), and part (c) is a textbook confidence interval calculation. All steps are routine with no problem-solving insight required, making it slightly easier than average. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.05a Sample mean distribution: central limit theorem5.05d Confidence intervals: using normal distribution |
3. A woodwork teacher measures the width, $w \mathrm {~mm}$, of a board. The measured width, $X \mathrm {~mm}$, is normally distributed with mean $w \mathrm {~mm}$ and standard deviation 0.5 mm .
\begin{enumerate}[label=(\alph*)]
\item Find the probability that $X$ is within 0.6 mm of $w$.
The same board is measured 16 times and the results are recorded.
\item Find the probability that the mean of these results is within 0.3 mm of $w$.
Given that the mean of these 16 measurements is 35.6 mm ,
\item find a $98 \%$ confidence interval for $w$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2010 Q3 [10]}}