The masses, in grams, of large and small packets of Maxwheat cereal have the independent distributions N(410.0, 3.6²) and N(206.0, 3.7²) respectively.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

1. [B1] E(D) = 410-2(206) = -2 SOI. OE using 2S-L.
2. [B1] Var(D) = 3.6^2 + 4 × 3.7^2 [= 67.72] SOI
3. [M1] (0-(-2)) / sqrt(67.72) [= 0.243]
4. [M1] For standardising using their values.
5. [M1] 1 – Φ(their ‘0.243')
6. [M1] For probability area consistent with their values.
7. [A1] = 0.404 (3 sf) As final answer.
8. [B1] TL ~N(4100, 10×3.6^2) Ts ~ N(4120, 20×3.7^2)
9. [B1] One of N(4100, 129.6) or N(4120, 273.8) USED (unchanged) in a standardising equation.
10. [M1] (4080-4100) / sqrt(129.6) (= -1.757)
11. [M1] Standardising with either their N(4100, 129.6) or N(4120, 273.8) or their N(.......) (could be from a combination).
12. [M1] 1 – Φ(‘−1.757') = Φ(1.757) and 1 – Φ(‘−2.417') = Φ(2.417)
13. [M1] One area consistent with their working (could be from a combination). Do not ISW.
14. [A1] = 0.9605 or 0.961 and = 0.9921 or 0.9922 or 0.992
15. [A1] Both of these correct. Do not ISW.
16. [M1] 0.6 × 'their 0.9605' + 0.4 × 'their 0.9921'
17. [M1] Must be using probabilities.
18. [A1] = 0.973 (3 sf)