Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
A filling machine packs rice into bags whose weights follow a normal distribution with mean $1.04\,\text{kg}$ and standard deviation $0.017\,\text{kg}$. The factory manager wants to increase the number of packets produced. He alters the machine settings so that the standard deviation stays unchanged, but the mean becomes $\mu\,\text{kg}$. For this new mean, the probability that a packet has weight less than $1\,\text{kg}$ is $0.0388$.
(i)[3]
Determine the probability that a packet selected at random weighs less than $1\,\text{kg}$.
(ii)[1]
From $1000\,\text{kg}$ of rice, how many packets of rice would the machine fill on average?
(iii)[3]
Find the value of $\mu$.
(iv)[1]
From $1000\,\text{kg}$ of rice, how many packets of rice would the machine now fill on average?
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate standardising $Z=\frac{1-1.04}{0.017}$” …