Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

The diameters of apples in an orchard are normally distributed, with mean $5.7\text{ cm}$ and standard deviation $0.8\text{ cm}$. Apples whose diameters lie between $4.1\text{ cm}$ and $5.0\text{ cm}$ may be used for toffee apples.
(i)[3]

Find the probability that a randomly chosen apple can be used as a toffee apple.

(ii)[5]

$250$ apples are selected at random. Use an appropriate approximation to determine the probability that fewer than $50$ can be used as toffee apples.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correctly standardise to get $z$-values, for example $z=-2$ or $z=-0.875$.

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI