A-LevelMathematicsProbability and statistics9709/61 · May/June 2022 · Q35 Marks
The lengths, in centimetres, of two types of insect, A and B, are modelled by the random variables X ~ N(6.2, 0.36) and Y ~ N(2.4, 0.25) respectively.
- (a)Find the probability that the length of a randomly chosen type A insect is greater than the sum of the lengths of 3 randomly chosen type B insects.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] D = X - (Y₁ + Y₂ + Y₃) OE E(D) = 6.2 - 2.4 × 3 [= -1] OE Give at early stage
- [B1] Var(D) = 0.36 + 3 × 0.25 [= 1.11] Give at early stage
- [M1] (0 - (-1)) / √'1.11' [= 0.949] No standard deviation/variance mixes Var must come from a combination attempt
- [M1] 1 - Φ('0.949') Area consistent with their values
- [A1] = 0.171 (3 s.f.)
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