| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI with two different confidence levels same sample |
| Difficulty | Standard +0.3 This is a straightforward reverse-engineering problem using standard confidence interval formulas. Students need to work backwards from the given interval to find σ, then use it to find c. It requires only routine manipulation of the CI formula X̄ ± z(σ/√n) with no conceptual difficulty beyond standard S3 material. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)5.05d Confidence intervals: using normal distribution |
5. A factory produces steel sheets whose weights, $X \mathrm {~kg}$, have a normal distribution with an unknown mean $\mu \mathrm { kg }$ and known standard deviation $\sigma \mathrm { kg }$.
A random sample of 25 sheets gave both a
\begin{itemize}
\item $95 \%$ confidence interval for $\mu$ of $( 30.612,31.788 )$
\item $c \%$ confidence interval for $\mu$ of $( 30.66,31.74 )$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\sigma$
\item Find the value of $c$, giving your answer correct to 3 significant figures.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2018 Q5 [7]}}