| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Difficulty | Challenging +1.2 This question requires understanding of linear combinations of normal variables and independence assumptions. Part (a) involves forming 3X - Y and finding P(3X - Y < 0), which requires careful handling of means and variances. Part (b) requires summing 8 independent cars and 3 independent lorries. While the concepts are standard S3 material, the multi-step variance calculations and the non-trivial setup in part (a) elevate this above routine exercises, though it remains a straightforward application of taught techniques without requiring novel insight. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)5.04a Linear combinations: E(aX+bY), Var(aX+bY)5.04b Linear combinations: of normal distributions |
5. The weights, in kg , of cars may be assumed to follow the normal distribution $\mathrm { N } \left( 1000,250 ^ { 2 } \right)$. The weights, in kg , of lorries may be assumed to follow the normal distribution $\mathrm { N } \left( 2800,650 ^ { 2 } \right)$.
A lorry and a car are chosen at random.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that the lorry weighs more than 3 times the weight of the car.
A ferry carries vehicles across a river. The ferry is designed to carry a maximum weight of 20000 kg .
\item One morning, 8 cars and 3 lorries drive on to the ferry. Find the probability that their total weight will exceed the recommended maximum weight of 20000 kg .
\item State a necessary assumption needed for the calculation in part (b).
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2018 Q5 [12]}}