Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
In a particular forest, tree heights are grouped as tall, medium or small. Their heights may be represented by a normal distribution with mean $20\,\text{m}$ and standard deviation $5\,\text{m}$. Any tree with height below $14\,\text{m}$ is put into the small group.
(a)[4]
If $150$ trees are chosen at random from this forest, how many would you expect to be small?
(b)[3]
Trees in this forest are described as tall if their height is at least $h\,\text{m}$. $25\%$ of the trees are tall. Determine the value of $h$.
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 $z=\frac{14-20}{5}$.” …