| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Expectation and variance with context application |
| Difficulty | Easy -1.2 This is a straightforward application of linear transformations and sums of independent random variables using standard formulas (E(aX)=aE(X), Var(aX)=a²Var(X), and properties of sums). Requires only direct substitution into well-known results with no problem-solving or conceptual insight needed. |
| Spec | 5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Mean \(= 115\) | B1 | |
| \(SD = 40\) | B1 | |
| 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Mean \(= 15 \times 115 = 1725\) | B1ft | |
| \(15 \times 40^2 = 24000\) | M1 | or \(SD = \sqrt{15} \times 40\), ft their (i) |
| \(SD = \sqrt{24000} = 155\) cents (3 sf) | A1 | Accept \(\sqrt{24000}\); allow correct answers in dollars |
| 3 |
## Question 1:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Mean $= 115$ | **B1** | |
| $SD = 40$ | **B1** | |
| | **2** | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Mean $= 15 \times 115 = 1725$ | **B1ft** | |
| $15 \times 40^2 = 24000$ | **M1** | or $SD = \sqrt{15} \times 40$, ft their (i) |
| $SD = \sqrt{24000} = 155$ cents (3 sf) | **A1** | Accept $\sqrt{24000}$; allow correct answers in dollars |
| | **3** | |
---1 At an internet café, the charge for using a computer is 5 cents per minute. The number of minutes for which people use a computer has mean 23 and standard deviation 8.\\
(i) Find, in cents, the mean and standard deviation of the amount people pay when using a computer.\\
(ii) Each day, 15 people use computers independently. Find, in cents, the mean and standard deviation of the total amount paid by 15 people.\\
\hfill \mbox{\textit{CAIE S2 2019 Q1 [5]}}