| 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 .\\
(i) 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 .\\
(ii) Use the confidence interval found in part (i) to comment on this claim.\\
\hfill \mbox{\textit{CAIE S2 2017 Q4 [4]}}