May/June 2026 Paper 63

2026 · 6 questions · 14 parts · 50 marks

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Context for question 6

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 N (25.5, 0.07)

and

Y \sim N (26.0, 0.08)

6(a)Linear Combinations Random VariablesHard5 marks

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.

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Probability

6(b)Linear Combinations Random VariablesHard5 marks

The mass of 1 litre of ingredient A is

m kg

and the mass of 1 litre of ingredient B is

1.5 m kg

, where

m

is a constant. 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

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m