Cambridge A Level Mathematics 9709 — 2008 Oct/Nov Paper 7 · Variant 1

3 Weights of garden tables are normally distributed with mean 36 kg and standard deviation 1.6 kg. Weights of garden chairs are normally distributed with mean 7.3 kg and standard deviation 0.4 kg. Find the probability that the total weight of 2 randomly chosen tables is more than the total weight of 10 randomly chosen chairs. [5]

Mark scheme:   1 A1 Correct integration ignore limits  3  1

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7 The time in hours taken for clothes to dry can be modelled by the continuous random variable with probability density function given by k √t 1 ≤t ≤4, f(t) = 0 otherwise, where k is a constant. (i) Show that k = 14.3 [3] (ii) Find the mean time taken for clothes to dry. [4] (iii) Find the median time taken for clothes to dry. [3] (iv) Find the probability that the time taken for clothes to dry is between the mean time and the median time. [2]

Mark scheme: Attempt to solve an equation in m, = 0.5 7 7 M1 m = 2.73 hours Correct answer (aef) A1 [3] .2726 5.0  .2 726 5.1 .2657 5.1  = − M1 Attempt to integrate using their mean and median(iv) ∫ kt dt 7 7 .2657   as limits = 0.0243 A1 [2] Correct answer accept between 0.0241 and 0.0257

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