| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2008 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Difficulty | Standard +0.3 This is a straightforward application of linear combinations of normal distributions requiring students to form L - 2S and L - 2S distributions, calculate their means and variances using standard formulas, then perform routine normal probability calculations. While it requires careful setup and understanding of independence, it's a standard S3 exercise with no novel insight needed. |
| Spec | 5.04b Linear combinations: of normal distributions |
4 Eezimix flour is sold in small bags of weight $S$ grams, where $S \sim \mathrm {~N} \left( 502.1,0.31 ^ { 2 } \right)$. It is also sold in large bags of weight $L$ grams, where $L \sim \mathrm {~N} \left( 1004.9,0.58 ^ { 2 } \right)$.\\
(i) Find the probability that a randomly chosen large bag weighs at least 1 gram more than two randomly chosen small bags.\\
(ii) Find the probability that a randomly chosen large bag weighs less than twice the weight of a randomly chosen small bag.
\hfill \mbox{\textit{OCR S3 2008 Q4 [11]}}