| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Same variable, two observations |
| Difficulty | Standard +0.3 This is a standard application of linear combinations of normal random variables with straightforward calculations. Part (a) requires finding the distribution of X₁-X₂ (variance = 5²+5² = 50), then a normal probability calculation. Parts (b) and (c) involve summing independent normals using standard formulas. While it requires understanding of the theory, the execution is routine for S3 level with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.04a Linear combinations: E(aX+bY), Var(aX+bY)5.04b Linear combinations: of normal distributions |
The weights of eggs are normally distributed with mean 60g and standard deviation 5g
Sairah chooses 2 eggs at random.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that the difference in weight of these 2 eggs is more than 2g
(5)
Sairah is packing eggs into cartons. The weight of an empty egg carton is normally distributed with mean 40g and standard deviation 1.5g
\item Find the distribution of the total weight of a carton filled with 12 randomly chosen eggs.
(3)
\item Find the probability that a randomly chosen carton, filled with 12 randomly chosen eggs, weighs more than 800g
(2)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2016 Q4}}