A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2020 · Q610 Marks

The volumes, in millilitres, of large and small cups of tea are modelled by the distributions N(200, 30) and N(110, 20) respectively.

(a)Find the probability that the total volume of a randomly chosen large cup of tea and a randomly chosen small cup of tea is less than 300 ml.[4]
(b)Find the probability that the volume of a randomly chosen large cup of tea is more than twice the volume of a randomly chosen small cup of tea.[6]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

[B1] N(310, 50); SOI
[M1] (300 - '310') / sqrt('50') (= -1.414); Standardise using their values
[M1] Φ(‘-1.414’) = 1 − Φ(‘1.414’); Area consistent with their values
[A1] = 0.0786 or 0.0787 (3 sf); As final answer
[M1] P(L - 2S > 0); OE SOI
[B1] E(X) = 200 - 2*110 or = – 20; OE seen
[B1] Var = 30 + 2² * 20 or = 110; Seen
[M1] (0 - '-20') / sqrt('110') (= 1.907); Standardising with their values. Mean and variance must come from a combination attempt.
[M1] 1 – Ф('1.907'); Correct area consistent with their working
[A1] = 0.0283 (3 sf); Final answer

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source: A-Level Mathematics, Feb/Mar 2020 Paper 6 Variant 2, question 6.

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