| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 6 |
| Topic | Linear combinations of normal random variables |
| Difficulty | Standard +0.3 This is a standard Further Statistics question on linear combinations of normal distributions. Part (i) requires finding the distribution of 6J + 8K (straightforward application of variance rules for independent normals), then a single normal probability calculation. Part (ii) requires rearranging K > 0.75J to K - 0.75J > 0, finding this distribution, and calculating another normal probability. Both parts are routine applications of well-practiced techniques with no conceptual surprises, making this slightly easier than average for A-level. |
| Spec | 2.04f Find normal probabilities: Z transformation5.04b Linear combinations: of normal distributions |
The mass $J$ kg of a bag of randomly chosen Jersey potatoes is a normally distributed random variable with mean 1.00 and standard deviation 0.06. The mass $K$ kg of a bag of randomly chosen King Edward potatoes is an independent normally distributed random variable with mean 0.80 and standard deviation 0.04.
\begin{enumerate}[label=(\roman*)]
\item Find the probability that the total mass of 6 bags of Jersey potatoes and 8 bags of King Edward potatoes is greater than 12.70 kg. [3]
\item Find the probability that the mass of one bag of King Edward potatoes is more than 75\% of the mass of one bag of Jersey potatoes. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2017 Q2 [6]}}