| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2012 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Expectation and variance with context application |
| Difficulty | Moderate -0.8 This is a straightforward application of standard results for linear combinations of independent random variables: E(aX + bY) = aE(X) + bE(Y) and Var(aX + bY) = a²Var(X) + b²Var(Y). The question requires only direct substitution of given values with no problem-solving or conceptual insight, making it easier than average. |
| Spec | 5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
Question 2:
B1 $(0.75 \times 54.8 + 0.25 \times 82.4 =) 61.7$
M1 $0.75 \times 16.0^2 + 0.25 \times 4.8^2$ $(= 145.44)$
A1 sd $= 12.1$ (3 sfs)
No need for $\sqrt{}$ for M12 An examination consists of a written paper and a practical test. The written paper marks ( $M$ ) have mean 54.8 and standard deviation 16.0. The practical test marks ( $P$ ) are independent of the written paper marks and have mean 82.4 and standard deviation 4.8. The final mark is found by adding $75 \%$ of $M$ to $25 \%$ of $P$. Find the mean and standard deviation of the final marks for the examination. [3]
\hfill \mbox{\textit{CAIE S2 2012 Q2 [3]}}