Mathematics 9709 · AS & A Level · Linear combinations of random variables

Linear combinations of random variables — practice question

The masses, measured in kilograms, of female and male animals of a particular species follow the distributions $N(102, 27^2)$ and $N(170, 55^2)$ respectively.
(main)[6]

Calculate the probability that a female chosen at random has a mass less than half the mass of a male chosen at random.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Introduce a combined variable such as $F - 0.5M$.

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