Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The heights of school desks follow a normal distribution with mean $69\,\text{cm}$ and standard deviation $\sigma\,\text{cm}$. It is given that $15.5\%$ of the desks are taller than $70\,\text{cm}$.
(i)[3]
Determine the value of $\sigma$.
(ii)[5]
When Jodu sits at a desk, the height of his knees above the floor is $58\,\text{cm}$. A desk is comfortable for Jodu provided his knees are at least $9\,\text{cm}$ below the top of the desk. Jodu’s school has $300$ desks. Calculate an estimate of how many of these desks are comfortable for Jodu.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate $z$-value determined, for example $z=1.015$” …