Cambridge A Level Mathematics 9709 — 2015 May/June Paper 6 · Variant 3

1 The weights, in grams, of onions in a supermarket have a normal distribution with mean - and standard deviation 22. The probability that a randomly chosen onion weighs more than 195 grams is 0.128. Find the value of -. [3]

Mark scheme: 1 z = 1.136 B1 ± 1.136 seen, not ±1.14, 195 − µ 1.136 = M1 Standardising, no cc no sq rt, 22 equated to their z not 0.128 or 0.872 µ = 170 A1 [3] Correct answer, nfww

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2 When Joanna cooks, the probability that the meal is served on time is 15. The probability that the kitchen is left in a mess is 35. The probability that the meal is not served on time and the kitchen is not left in a mess is 10.3 Some of this information is shown in the following table. Kitchen left Kitchen not Total in a mess left in a mess Meal served on time 1 5 Meal not served on time 3 10 Total 1 (i) Copy and complete the table. [3] (ii) Given that the kitchen is left in a mess, find the probability that the meal is not served on time. [2]

Mark scheme: 2 (i) All values may be decimals or % Kitchen Kitchen Total B1 2 probabilities correct mess not mess On time 1/10 1/10 B1 2 further probabilities correct Not on 1/2 4/5 time Total 3/5 4/10 B1 [3] 2 further probabilities correct

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3 On a production line making cameras, the probability of a randomly chosen camera being substandard is 0.072. A random sample of 300 cameras is checked. Find the probability that there are fewer than 18 cameras which are substandard. [5]

Mark scheme: 3

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6 Seventy samples of fertiliser were collected and the nitrogen content was measured for each sample. The cumulative frequency distribution is shown in the table below. Nitrogen content ≤3.5 ≤3.8 ≤4.0 ≤4.2 ≤4.5 ≤4.8 Cumulative frequency 0 6 18 41 62 70 (i) On graph paper draw a cumulative frequency graph to represent the data. [3] (ii) Estimate the percentage of samples with a nitrogen content greater than 4.4. [2] (iii) Estimate the median. [1] (iv) Construct the frequency table for these results and draw a histogram on graph paper. [5]

Mark scheme: 6 (i) B1 Uniform axes cf and nitrogen content labelled, at least 0 to 70 and 3.5 to 4.8 seen M1 5 points plotted correctly on graph paper 3.5 3.8 4.0 4.2 4.5 4.8 3.5 4.0 4.5 5.0 nitrogen 0 6 18 41 62 70 content A1 [3] All points correct and a reasonable curve (condone 1 missed point) or line segments. (ii) 70 – their 55 = 15 M1 Subt a value > 41 from 70 (or n/70, = 21.4% A1 [2] n<29) Correct ans, accept 18.5 – 22 (iii) median = 4.15 B1 [1] Accept 4.1< median < 4.2, nfww (iv) nit 3.5– 3.8– 4.0– 4.2– 4.5– M1 Attempt at freqs, at least 3 correct, cont 3.8 4.0 4.2 4.5 4.8 ignore labelling fr 6 12 23 21 8 fd 20 60 115 70 26.7 M1 Attempt at fd as f/cw only at least 3 correct FT fd (Accept f/cw × k) 120 100 A1 Correct heights seen on graph (plot at 4.8,27 A0)

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