AS & A Level Further Mathematics (9231) — October–November 2023, Paper 42

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Question 1 · 6 marks · Estimation - confidence interval for a difference of population means (large samples, z-distribution)

A factory produces small bottles of natural spring water. Two different machines, X and Y, are used to fill empty bottles with the water. A quality control engineer checks the…

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Question 2 · 8 marks · Chi-squared tests - expected frequencies from a Poisson model

The number of breakdowns on a particular section of road is recorded each day over a period of 90 days. It is suggested that the number of breakdowns follows a Poisson…

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Question 3 · 10 marks · Probability generating functions - forming the pgf of a discrete random variable

Toby has a bag which contains 6 red marbles and 3 green marbles. He randomly chooses 3 marbles from the bag, without replacement. The random variable X is the number of red…

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Question 4 · 10 marks · Continuous random variables - determining constants in a piecewise pdf

The diagram shows the continuous random variable X with probability density function f given by f(x) = (1/128)(4ax - bx^3) for 0 <= x <= 4, f(x) = c for 4 <= x <= 6, f(x) = 0…

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Question 5 · 16 marks · Non-parametric tests - Wilcoxon rank-sum test (two independent samples)

A company is deciding which of two machines, X and Y, can make a certain type of electrical component more quickly. The times taken, in minutes, to make one component of this type…

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