A-LevelMathematicsProbability and statistics9709/63 · May/June 2022 · Q410 Marks
Each box of Seeds & Raisins contains S grams of seeds and R grams of raisins. The weight of a box, when empty, is B grams. S, R and B are independent random variables, where S ~ N(300, 45), R ~ N(200, 25) and B ~ N(15, 4). A full box of Seeds & Raisins is chosen at random.
- (a)Find the probability that the total weight of the box and its contents is more than 500 grams.[5]
- (b)Find the probability that the weight of seeds in the box is less than 1.4 times the weight of raisins in the box.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] T~N(515, ..)
- [B1] Var = 45 + 25 + 4 = 74
- [M1] (500-'515') / √'74' [= -1.744]
- [M1] Φ('1.744')
- [A1] 0.959 or 0.96[0] (3 s.f.)
- [B1] E(S-1.4R) = 300-1.4x200 =20
- [B1] Var(S-1.4R) = 45 + 1.4^2×25 = 94
- [M1] (0-(20)) / √'94' [= -2.063]
- [M1] 1 – Φ('2.063')
- [A1] 0.0196 (3 s.f.)
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