Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
For children of this age, jump heights are normally distributed. On average, $8$ children out of $10$ can jump higher than $127\text{ cm}$, and $1$ child out of $3$ can jump higher than $135\text{ cm}$.
(a)[5]
Determine the mean and standard deviation of the heights the children can jump.
(b)[3]
Calculate the probability that a child chosen at random will be unable to jump a height of $145\text{ cm}$.
(c)[3]
Calculate the probability that at least $2$ of $8$ randomly selected children can jump more than $135\text{ cm}$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate $z$-values inserted into equations $0.431=\frac{135-\mu}{\sigma}$ and $-0.842=\frac{127-\mu}{\sigma}$” …