Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
A company makes large bags of pasta whose weights are normally distributed with mean $1.5\,\text{kg}$ and standard deviation $0.05\,\text{kg}$.
(a)[3]
Find the probability that a large bag of pasta chosen at random has a weight between $1.42\,\text{kg}$ and $1.52\,\text{kg}$.
(b)[3]
The weights of small bags of pasta made by the company are normally distributed with mean $0.75\,\text{kg}$ and standard deviation $\sigma\,\text{kg}$. It is observed that $68\%$ of these small bags weigh less than $0.9\,\text{kg}$. Find the value of $\sigma$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Standardisation used correctly, for example $P(1.42<X<1.52)=P\left(\frac{1.42-1.5}{0.05}<Z<\frac{1.52-1.5}{0.05}\right)$.” …