A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2020 · Q36 Marks

The masses, in kilograms, of female and male animals of a certain species have the distributions N(102, 27²) and N(170, 55²) respectively. Find the probability that a randomly chosen female has a mass that is less than half the mass of a randomly chosen male.

Find the probability that a randomly chosen female has a mass that is less than half the mass of a randomly chosen male.[6]

Mark scheme

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

[M1] SOI
[B1] for 102 - 0.5(170) (= 17) or 34
[B1] for 27^2 + 0.25 × 55^2 (= 1485.25) or 2^2 × 27^2 + 55^2 (= 5941)
[M1] Must have an attempt at combining F and M. No standard deviation/variance errors.
[M1] Correct area consistent with their figures.
[A1] Allow 0.33 if no greater accuracy given

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Oct/Nov 2020 Paper 6 Variant 1, question 3.

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