9709 P63 - Jun 2026 - Q6 - 10 marks
9199
One batch of a cake mixture contains \(X\) litres of ingredient A and \(Y\) litres of ingredient B, where \(X\) and \(Y\) have the independent distributions \(X\sim\mathrm N(25.5,0.07)\) and \(Y\sim\mathrm N(26.0,0.08)\).
(a) Find the probability that, in a randomly chosen batch of the mixture, the number of litres of ingredient A is greater than the number of litres of ingredient B. [5]
The mass of 1 litre of ingredient A is \(m\text{ kg}\) and the mass of 1 litre of ingredient B is \(1.5m\text{ kg}\), where \(m\) is a constant.
(b) Given that the probability that the total mass of a randomly chosen batch of the mixture is less than 70 kg is \(0.3\), find the value of \(m\). [5]
