Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The body-feather lengths of a given bird species are represented by a normal distribution. A researcher takes a random sample of $600$ body feathers from birds of this species and records that $63$ are shorter than $6\text{ cm}$ and $155$ exceed $12\text{ cm}$ in length.
(i)[5]
Determine estimates for the mean and standard deviation of the body-feather lengths of birds of this species.
(ii)[4]
For a random sample of $1000$ body feathers from birds of this species, how many would the researcher expect to have lengths more than $1$ standard deviation from the mean?
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “From $-1.253 = \frac{6-\mu}{\sigma}$ and $0.648 = \frac{12-\mu}{\sigma}$ (or matching $Z$-values)” …