A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2025 · Q15 Marks
The random variables X and Y have the independent distributions N(44, 16) and N(30, 9) respectively. Find P(X-Y < 15).
- Find P(X-Y < 15).[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.
- [B1] X-Y~N(44-30, .....) N(14, ....) or X-Y-15~ N(−1, ....) soi give at early stage.
- [B1] Var(X - Y) = 16 + 9 = 25 or sd = 5 SOI give at early stage.
- [M1] 15-'14'/√25' [= 0.2] Standardising with their values.
- [M1] Φ('0.2') For area consistent with their values.
- [A1] = 0.579 (3 sf)
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