Standard +0.3 This is a straightforward application of properties of linear combinations of random variables (variance of sums/differences). While it requires identifying that match mass = (full box - empty box)/50 and correctly applying variance rules, it's a standard S3 technique with clear setup. The 7 marks reflect multiple calculation steps rather than conceptual difficulty, making it slightly above average but routine for this module.
2 Boxes of matches contain 50 matches. Full boxes have mean mass 20.0 grams and standard deviation 0.4 grams. Empty boxes have mean mass 12.5 grams and standard deviation 0.2 grams. Stating any assumptions that you need to make, calculate the mean and standard deviation of the mass of a match. [7]
Assume \(F = E + M_1 + M_2 + \ldots + M_{50}\) where masses are independent and mass of empty box is independent of masses of matches
B1
For one relevant valid assumption
B1
For another relevant valid assumption
\(20.0 = 12.5 + 50\mu\) giving mean mass of a match is 0.15 grams
M1
For attempting \(E(F)\) in terms of \(\mu\)
A1
For correct value 0.15
\(0.4^2 = 0.2^2 + 50\sigma^2\)
M1
For attempting \(\text{Var}(F)\) as a sum
A1
For correct equation
Standard deviation is 0.049 grams
A1
7
Assume $F = E + M_1 + M_2 + \ldots + M_{50}$ where masses are independent and mass of empty box is independent of masses of matches | B1 | For one relevant valid assumption
| B1 | For another relevant valid assumption
$20.0 = 12.5 + 50\mu$ giving mean mass of a match is 0.15 grams | M1 | For attempting $E(F)$ in terms of $\mu$
| A1 | For correct value 0.15
$0.4^2 = 0.2^2 + 50\sigma^2$ | M1 | For attempting $\text{Var}(F)$ as a sum
| A1 | For correct equation
Standard deviation is 0.049 grams | A1 | 7 | For correct value 0.049
2 Boxes of matches contain 50 matches. Full boxes have mean mass 20.0 grams and standard deviation 0.4 grams. Empty boxes have mean mass 12.5 grams and standard deviation 0.2 grams. Stating any assumptions that you need to make, calculate the mean and standard deviation of the mass of a match. [7]
\hfill \mbox{\textit{OCR S3 Q2 [7]}}