Cambridge A Level Mathematics 9709 — 2013 May/June Paper 7 · Variant 2

5 Packets of cereal are packed in boxes, each containing 6 packets. The masses of the packets are normally distributed with mean 510 g and standard deviation 12 g. The masses of the empty boxes are normally distributed with mean 70 g and standard deviation 4 g. (i) Find the probability that the total mass of a full box containing 6 packets is between 3050 g and 3150 g. [5] (ii) A packet and an empty box are chosen at random. Find the probability that the mass of the packet is at least 8 times the mass of the empty box. [5]

Mark scheme: 5 (i) 6 × 510 + 70 = (3130) B1 6 × 122 + 42 = (880) B1 N(3130, 880) 3050−3130 (= – 2.697) 880 3150−3130 (= 0.674) M1 Both. With their mean and variance(≥0) Allow 880 without √ M1 Use of tables and attempt to find area consistent Φ(‘0.674’) – (1 – Φ(‘2.697’)) with their working (= 0.7499 – 0.0035) = 0.746 (3 sf) A1 [5] (ii) 510 – 8 × 70 =( – 50) B1 o.e. +50; 510/8 -70; – (510/8 – 70) 122 + 82 × 42 = (1168) B1 o.e. (12/8)² +4² P – 8C ~ N(– 50, 1168) 0 − ( − 50 ) (= 1.463) M1 For standardising with attempt “P-8C” oe with 1168 their mean and variance(≥0).Allow without √ M1 Use of tables and attempt to find area consistent 1 – Φ(‘1.463’) with their working = 0.0717 (3 s.f.) A1 [5] [Total: 10] GCE AS/A LEVEL – May/June 2013 9709 72

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