| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Two or more different variables |
| Difficulty | Challenging +1.2 This question requires understanding independence of normal variables, finding probabilities for two separate events, and multiplying them. While it involves multiple normal distribution calculations and the concept of independence, the steps are methodical and the setup is clearly guided by the question structure. It's moderately harder than average due to the multi-step nature and need to recognize independence, but doesn't require novel insight. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.04a Linear combinations: E(aX+bY), Var(aX+bY)5.04b Linear combinations: of normal distributions |
\begin{enumerate}
\item The weight of coffee in glass jars labelled 100 g is normally distributed with mean 101.80 g and standard deviation 0.72 g . The weight of an empty glass jar is normally distributed with mean 260.00 g and standard deviation 5.45 g . The weight of a glass jar is independent of the weight of the coffee it contains.
\end{enumerate}
Find the probability that a randomly selected jar weighs less than 266 g and contains less than 100 g of coffee. Give your answer to 2 significant figures.\\
(8 marks)\\
\hfill \mbox{\textit{Edexcel S1 Q1 [8]}}