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

Linear combinations of random variables — practice question

The building heights in a large city are modeled by a normal distribution with mean $18.3\,\text{m}$ and standard deviation $2.5\,\text{m}$.
(a)[4]

Determine the probability that the combined height of $5$ buildings selected at random in the city is greater than $95\,\text{m}$.

(b)[5]

Determine the probability that the difference between the heights of two buildings chosen at random in the city is less than $1\,\text{m}$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Distribution given with mean and variance as $N(91.5,31.25)$

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