Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
For kestrels, adult wingspans follow a normal distribution with mean $74.8\text{ cm}$ and standard deviation $3.2\text{ cm}$. A random sample of 120 adult kestrels is taken.
(a)[4]
Of these 120 adult kestrels, how many would you expect to have wingspan between $72.4\text{ cm}$ and $76.3\text{ cm}$?
(b)[5]
The masses of adult kestrels follow a normal distribution with mean $\mu\text{ kg}$ and standard deviation $\sigma\text{ kg}$. It is known that $20\%$ of adult kestrels have mass greater than $0.202\text{ kg}$ and $28\%$ have mass less than $0.185\text{ kg}$. Determine the value of $\mu$ and the value of $\sigma$.
(c)[3]
Find the probability that fewer than $3$ have mass greater than $0.202\text{ kg}$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Bounds standardised correctly, e.g. $P\left(\frac{72.4-74.8}{3.2}<Z<\frac{76.3-74.8}{3.2}\right)$.” …