Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

Buildings in one city-centre area are grouped by height into tall, medium or short. Their heights may be represented by a normal distribution with mean $50$ metres and standard deviation $16$ metres. Any building taller than $70$ metres is put in the tall category.
(a(i))[2]

Determine the probability that a building selected at random is tall.

(a(ii))[5]

The remaining buildings are split into medium and short so that the number of medium buildings is twice the number of short buildings. Determine the height below which buildings are classified as short.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Standardising with $z=\frac{70-50}{16}$ and writing the probability as $P(Z>1.25)$

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