Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
Each can of lemon juice should contain $440\,\text{ml}$ of juice. The actual amount of juice in a can is stated to be normally distributed with mean $445\,\text{ml}$ and standard deviation $3.6\,\text{ml}$.
(i)[3]
Determine the probability that a can chosen at random contains less than $440\,\text{ml}$ of juice.
(ii)[3]
It is stated that $94\%$ of the cans have juice amounts between $(445 - c)\,\text{ml}$ and $(445 + c)\,\text{ml}$. Determine the value of $c$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Convert to $P\left(z<\frac{440-445}{3.6}\right)$” …