Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Plastic drinking straws are made so that they will slot into drinks cartons with a hole in the top. A straw passes through the hole when its diameter is below $3\,\text{mm}$. The straw diameters follow a normal distribution with mean $2.6\,\text{mm}$ and standard deviation $0.25\,\text{mm}$.
(i)[3]
Select a straw at random. Find the probability that it fits into the hole in a drinks carton.
(ii)[5]
A random selection of $500$ straws is made. Use a suitable approximation to find the probability that at least $480$ straws fit into the holes in drinks cartons.
(iii)[1]
Justify the use of your approximation.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Standardising the value and writing $P\left(Z < \frac{3.0 - 2.6}{0.25}\right)$” …