Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
Company A makes bags of sugar. An inspector discovers that, on average, $10\%$ of the bags are underweight. $10$ of the bags are picked at random.
(a)[3]
Calculate the probability that fewer than $3$ of these bags are underweight.
(b)[3]
For company $B$, the weights of its sugar bags follow a normal distribution with mean $1.04\,\text{kg}$ and standard deviation $0.06\,\text{kg}$. Find the probability that one bag chosen at random from company $B$ has weight above $1.11\,\text{kg}$.
(c)[3]
For company $B$, $81\%$ of the bags of sugar have mass below $w\,\text{kg}$. Find the value of $w$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct binomial form for $P(0,1,2)$” …