Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
Trees in the Redian forest are grouped into tall, medium, or short categories according to their height. Their heights may be represented by a normal distribution with mean $40\text{ m}$ and standard deviation $12\text{ m}$. Any tree with height below $25\text{ m}$ is placed in the short category.
(a)[3]
Calculate the probability that a tree chosen at random is classed as short.
(b)[2]
Among the trees classed as tall or medium, one third are tall and two thirds are medium. Show that the probability that a randomly chosen tree is tall is $0.298$, correct to $3$ decimal places.
(c)[3]
Calculate the height above which trees are classed as tall.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly standardise by writing $P(X<25)=P\left(Z<\bfrac{25-40}{12}\right)$” …