Mathematics 9709 · AS & A Level · The normal distribution

The normal distribution — practice question

The masses, in kg, of bags of rice made by Anders are modelled by the distribution $N(2.02, 0.03^2)$.
(a)[3]

Determine the probability that a bag of rice chosen at random from those produced by Anders has a weight between $1.98\text{ kg}$ and $2.03\text{ kg}$.

(b)[4]

For bags of rice produced by Binders, the weights follow a normal distribution with mean $2.55\text{ kg}$ and standard deviation $\sigma\text{ kg}$. In a random sample of $5000$ of these bags, $134$ had weights greater than $2.6\text{ kg}$. Determine the value of $\sigma$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate standardisation of $P(1.98 < X < 2.03)$

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