Mathematics 9709 · AS & A Level · The normal distribution

The normal distribution — practice question

The heights, in metres, of white pine trees follow a normal distribution with mean $19.8$ and standard deviation $2.4$. In one forest, there are $450$ white pine trees.
(a)[4]

How many of these trees would you expect to be shorter than $18.2$ metres?

(b)[3]

The heights, in metres, of red pine trees follow a normal distribution with mean $23.4$ and standard deviation $\sigma$. It is given that $26\%$ of red pine trees are taller than $25.5$ metres. Find the value of $\sigma$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct standardisation using $Z=\frac{18.2-19.8}{2.4}$

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