A-LevelMathematicsProbability and statistics9709/63 · May/June 2024 · Q14 Marks
The random variable X has the distribution B (4000, 0.001).
- (a)Use a suitable approximating distribution to find P(2 < X < 5).[3]
- (b)Justify your approximating distribution in this case.[1]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [B1] [λ =] 4
- [M1] e⁻⁴ (4²/2 + 4³/6 + 4⁴/24) or e⁻⁴ (8 + 10.67 + 10.67) or 0.1465 + 0.19537 + 0.19537
- [A1] = 0.537 (3sf)
- [B1] n = 4000 > 50 and either np = 4 < 5 or p = 0.001 < 0.1
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