| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2024 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | Known variance (z-distribution) |
| Difficulty | Moderate -0.8 Part (a) is a standard confidence interval calculation using known σ and the normal distribution—pure routine application of the formula with no conceptual challenge. Part (b) tests understanding of what a confidence interval means, which is a common misconception question but requires only brief recall of the correct interpretation rather than any calculation or problem-solving. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(z = 2.054\) or \(2.055\) | B1 | Accept 3 sf if nothing better seen (\(2.05\) or \(2.06\)) |
| \(1.42 \pm z\dfrac{0.35}{\sqrt{150}}\) | M1 | Must be a \(z\) value |
| \(1.36\) to \(1.48\) [m] (3 sf) | A1 | Correct working only. Must be an interval |
| 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| No. CI is about mean, not individual values. | B1 | Or similar. Need both. |
| 1 |
## Question 1:
### Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $z = 2.054$ or $2.055$ | **B1** | Accept 3 sf if nothing better seen ($2.05$ or $2.06$) |
| $1.42 \pm z\dfrac{0.35}{\sqrt{150}}$ | **M1** | Must be a $z$ value |
| $1.36$ to $1.48$ [m] (3 sf) | **A1** | Correct working only. Must be an interval |
| | **3** | |
### Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| No. CI is about mean, not individual values. | **B1** | Or similar. Need both. |
| | **1** | |
---1 The heights of a certain species of deer are known to have standard deviation 0.35 m . A zoologist takes a random sample of 150 of these deer and finds that the mean height of the deer in the sample is 1.42 m .
\begin{enumerate}[label=(\alph*)]
\item Calculate a 96\% confidence interval for the population mean height.
\item Bubay says that $96 \%$ of deer of this species are likely to have heights that are within this confidence interval.
Explain briefly whether Bubay is correct.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2024 Q1 [4]}}