Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
Adult raccoons of one particular species have tail lengths that are normally distributed, with mean $28\text{ cm}$ and standard deviation $3.3\text{ cm}$.
(a)[4]
Find the probability that a randomly selected adult raccoon of this species has a tail length between $23\text{ cm}$ and $35\text{ cm}$.
(b)[3]
The masses of adult raccoons of this species are normally distributed, with mean $8.5\text{ kg}$ and standard deviation $\sigma\text{ kg}$. $75\%$ of adult raccoons of this species have mass greater than $7.6\text{ kg}$. Find the value of $\sigma$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly standardise to $P(-1.515<Z<2.121)$ using $\mu=28$ and $\sigma=3.3$.” …