A-LevelMathematicsProbability and statistics9709/63 · May/June 2020 · Q69 Marks
The length, X centimetres, of worms of a certain type is modelled by the probability density function f(x) = { (1/125)(10-x)(x - 5) 5 ≤ x ≤ 10, 0 otherwise. }
- (a)State the value of E(X).[1]
- (b)Find Var(X).[3]
- (c)Two worms of this type are chosen at random. Find the probability that exactly one of them has length less than 6 cm.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] (a) 7.5
- [M1] (b) (6/125) ∫ (–x⁴ + 15x³ – 50x²)dx, from 5 to 10
- [M1] (b) (6/125) [–x⁵/5 + 15x⁴/4 – 50x³/3] evaluated from 5 to 10 – ‘7.5’²
- [A1] (b) 1.25 (3 sf)
- [M1] (c) (6/125) ∫ (−x² + 15x – 50)dx from 5 to 6
- [M1] (c) (6/125) [–x³/3 + 15x²/2 – 50x] evaluated from 5 to 6
- [A1] (c) (6/125)(–102 + 625/6) oe = 0.104
- [M1] (c) 2 × (‘0.104’) × (1 – ‘0.104’)
- [A1ft] (c) 0.186 (3 sf)
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