AS & A Level Further Mathematics (9231) — October–November 2024, Paper 41

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Question 1 · 6 marks · Estimation (confidence interval for the difference between two population means, large independent samples, z-distribution)

Ellie is investigating the heights of two types of beech tree, A and B, in a certain region. She has chosen a random sample of 60 beech trees of type A in the region, recorded…

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Question 2 · 9 marks · Non-parametric tests (Wilcoxon matched-pairs signed-rank test, small sample, tabulated critical value)

A school with a large number of students is updating its logo. Each student has designed a new logo and two teachers have each awarded a mark out of 50 for each logo. The marks…

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Question 3 · 8 marks · Goodness of fit (calculating Poisson expected frequencies)

A statistician believes that the number of telephone calls received by an advice centre in a 10-minute interval can be modelled by the Poisson distribution Po(1.9). The number of…

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Question 4 · 10 marks · Continuous random variables (sketching a piecewise probability density function)

The continuous random variable X has probability density function f given by f(x) = kx^3 for 0 <= x < 1, f(x) = k(5 - x) for 1 <= x <= 5, f(x) = 0 otherwise, where k is a…

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Question 5 · 9 marks · Probability generating functions (constructing the pgf of a sum of independent Bernoulli trials)

Nikita has three coins. One coin is fair, one coin is biased so that the probability of obtaining a head is 1/3 and the third coin is biased so that the probability of obtaining a…

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Question 6 · 8 marks · Hypothesis tests (two-sample t-test for a difference of means, normal populations with equal unknown variances, pooled estimate)

Ansal is investigating the wingspans of Monarch butterflies in two different regions, X and Y. He takes a random sample of 8 Monarch butterflies from region X and records their…

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