Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
The lengths of the leaves on a certain kind of tree are represented by a normal distribution. A scientist takes a random sample of $500$ leaves from this tree species and records that $42$ are shorter than $4\text{ cm}$ and $100$ exceed $10\text{ cm}$ in length.
(a)[5]
Determine estimates for the mean and standard deviation of the lengths of leaves from this tree species.
(b)[4]
Find the number of these leaves that the scientist would expect to have lengths, in cm, between $\mu - 2\sigma$ and $\mu + 2\sigma$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtains $z_1 = \frac{4-\mu}{\sigma} = -1.378$” …