Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The letter weights sent by one business follow a normal distribution with mean $20\,\mathrm{g}$. It is given that $94\%$ of the letters have weights lying within $12\,\mathrm{g}$ of the mean.
(i)[3]
Find the standard deviation of the letter weights.
(ii)[3]
Find the probability that a letter chosen at random weighs more than $13\,\mathrm{g}$.
(iii)[3]
Find the probability that, in a random sample of $7$ letters, at least $2$ have weights which are more than $12\,\mathrm{g}$ above the mean.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Take $z=\frac{32-20}{\sigma}$ with $z=1.882$ or $1.881$” …