| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2017 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI from summary stats |
| Difficulty | Moderate -0.3 This is a straightforward confidence interval question requiring standard formula application (z-value lookup, calculation) followed by basic interpretation. Part (i) is routine bookwork; part (ii) requires only checking if 300 lies in the interval. Slightly easier than average due to minimal problem-solving and being a standard textbook exercise. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(300.1 \pm z \times \frac{0.9}{\sqrt{75}}\) | M1 | allow any value of \(z\) |
| \(z = 2.576\) | B1 | allow \(2.574\) to \(2.579\) |
| \(299.83\) to \(300.37\) (2 dps) | A1 | answer must be seen to 2 dps; need an interval |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| CI includes \(300\) so claim supported or justified or probably true | B1 FT | or equivalent; FT from CI in (i) |
| Total: 1 |
## Question 4(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $300.1 \pm z \times \frac{0.9}{\sqrt{75}}$ | M1 | allow any value of $z$ |
| $z = 2.576$ | B1 | allow $2.574$ to $2.579$ |
| $299.83$ to $300.37$ (2 dps) | A1 | answer must be seen to 2 dps; need an interval |
| **Total: 3** | | |
## Question 4(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| CI includes $300$ so claim supported or justified or probably true | B1 FT | or equivalent; FT from CI in (i) |
| **Total: 1** | | |
---4 The lengths, in millimetres, of rods produced by a machine are normally distributed with mean $\mu$ and standard deviation 0.9. A random sample of 75 rods produced by the machine has mean length 300.1 mm .\\
\begin{enumerate}[label=(\roman*)]
\item Find a $99 \%$ confidence interval for $\mu$, giving your answer correct to 2 decimal places.\\
The manufacturer claims that the machine produces rods with mean length 300 mm .
\item Use the confidence interval found in part (i) to comment on this claim.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2017 Q4 [4]}}