| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2018 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Known variance confidence interval |
| Difficulty | Moderate -0.8 This is a straightforward confidence interval calculation using known variance and large sample size. Part (i) requires only direct application of the formula z*σ/√n with a standard z-value lookup, and part (ii) asks for simple recall of the normality/CLT assumption. No problem-solving or conceptual insight needed beyond textbook procedure. |
| Spec | 5.05a Sample mean distribution: central limit theorem5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(176 \pm z \times \frac{7.2}{\sqrt{200}}\) | M1 | need correct form must be z |
| \(z = 2.24\) | B1 | allow 2.241 and 2.242 |
| 175 to 177 | A1 | cwo |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Sample random | B1 | oe. both words essential |
| Total: 1 |
## Question 1:
**Part (i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $176 \pm z \times \frac{7.2}{\sqrt{200}}$ | M1 | need correct form must be z |
| $z = 2.24$ | B1 | allow 2.241 and 2.242 |
| 175 to 177 | A1 | cwo |
| **Total: 3** | | |
**Part (ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Sample random | B1 | oe. both words essential |
| **Total: 1** | | |
---1 The standard deviation of the heights of adult males is 7.2 cm . The mean height of a sample of 200 adult males is found to be 176 cm .\\
(i) Calculate a $97.5 \%$ confidence interval for the mean height of adult males.\\
(ii) State a necessary condition for the calculation in part (i) to be valid.\\
\hfill \mbox{\textit{CAIE S2 2018 Q1 [4]}}