| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Mixed sum threshold probability |
| Difficulty | Standard +0.8 This Further Maths statistics question requires understanding of linear combinations of normal variables and forming inequalities from verbal descriptions. Part (i) is straightforward application of sum properties, but part (ii) requires translating '75% of' into K > 0.75J, then finding the distribution of K - 0.75J, which demands more conceptual insight than routine application. |
| Spec | 5.04b Linear combinations: of normal distributions |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (i) | (cid:166)J (cid:14)(cid:166)K ~N(12.4, 0.0344) |
| P(cid:11)(cid:33)12.7(cid:12)(cid:32)1(cid:16)0.9471(cid:32)0.0529 | M1 |
| Answer | Marks |
|---|---|
| [3] | 1.1a |
| Answer | Marks |
|---|---|
| 1.1 | m |
| Answer | Marks | Guidance |
|---|---|---|
| awrt 0.053 BC | 0.232 or 0.68: M1A0 | |
| 2 | (ii) | p |
| Answer | Marks |
|---|---|
| P((cid:33)0)(cid:32)(cid:41)(0.08305)(cid:32)0.7969 | e |
| Answer | Marks |
|---|---|
| [3] | 1.1a |
| Answer | Marks |
|---|---|
| 1.1 | Or 4K(cid:16)3J N(cid:11)0.2,...(cid:12) |
| Answer | Marks | Guidance |
|---|---|---|
| 2(i) | 3 | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 2(ii) | 3 | 0 |
Question 2:
2 | (i) | (cid:166)J (cid:14)(cid:166)K ~N(12.4, 0.0344)
P(cid:11)(cid:33)12.7(cid:12)(cid:32)1(cid:16)0.9471(cid:32)0.0529 | M1
A1
c
A1
[3] | 1.1a
i1.1
1.1 | m
Consider the sum ~N(12.4,...
Standard deviation or variance correct
awrt 0.053 BC | 0.232 or 0.68: M1A0
2 | (ii) | p
K(cid:16)0.75J N(0.05, 0.003625)
P((cid:33)0)(cid:32)(cid:41)(0.08305)(cid:32)0.7969 | e
M1
A1
A1
[3] | 1.1a
1.1
1.1 | Or 4K(cid:16)3J N(cid:11)0.2,...(cid:12)
Standard deviation or variance correct
0.0043 or 0.085: M1A0
awrt 0.797 BC
--- 2(i) ---
2(i) | 3 | 0 | 0 | 0 | 3
--- 2(ii) ---
2(ii) | 3 | 0 | 0 | 0 | 32 The mass $J \mathrm {~kg}$ 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 Kkg 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 .\\
(i) 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 .\\
(ii) 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.
\hfill \mbox{\textit{OCR Further Statistics Q2 [6]}}