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Find the chance that the length of one randomly selected type $A$ insect exceeds the combined lengths of 3 randomly selected type $B$ insects.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The lengths, measured in centimetres, of two insect types, $A$ and $B$, are represented by the random variables $X \sim N(6.2, 0.36)$ and $Y \sim N(2.4, 0.25)$, respectively.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Introduces $D = X - (Y_1 + Y_2 + Y_3)$ and calculates $E(D) = 6.2 - 2.4 \times 3 = -1$” …
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