Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
A farmer observes that the weights of sheep on his farm follow a normal distribution with mean $66.4\,\text{kg}$ and standard deviation $5.6\,\text{kg}$.
(a(i))[5]
Estimate how many sheep have weights between $70\,\text{kg}$ and $72.5\,\text{kg}$.
(a(ii))[2]
The fraction of sheep weighing less than $59.2\,\text{kg}$ matches the fraction weighing more than $y\,\text{kg}$. Find the value of $y$.
(a(iii))[3]
A different farmer finds that the weights of sheep on his farm follow a normal distribution with mean $\mu\,\text{kg}$ and standard deviation $4.92\,\text{kg}$. $25\%$ of these sheep are heavier than $67.5\,\text{kg}$. Find the value of $\mu$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applying standardisation to $70$ and $72.5$ in order to find $z_1$ and $z_2$” …