AS & A Level Mathematics (9709) — May–June 2023, Paper 62

7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

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Question 1 · 3 marks · Estimation (confidence interval for a population proportion)

In a survey of 200 randomly chosen students from a certain college, 23% of the students said that they owned a car. Calculate an approximate 93% confidence interval for the…

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Question 2 · 5 marks · The Poisson distribution (mean and variance)

The random variable W has a Poisson distribution. State the relationship between E(W) and Var(W).

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Question 3 · 8 marks · Estimation (unbiased estimates of population mean and variance)

The masses, in kilograms, of newborn babies in country A are represented by the random variable X, with mean μ and variance σ². The masses of a random sample of 500 newborn babies…

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Question 4 · 10 marks · The Poisson distribution (conditions for a Poisson model)

The number, X, of books received at a charity shop has a constant mean of 5.1 per day. State, in context, one condition for X to be modelled by a Poisson distribution.

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Question 5 · 11 marks · Linear combinations of independent Normal variables

Two random variables X and Y have the independent distributions N(7, 3) and N(6, 2) respectively. A random value of each variable is taken. Find the probability that the two…

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Question 6 · 5 marks · Hypothesis tests (Type I error, binomial distribution)

When a child completes an online exercise called a Mathlit, they might be awarded a medal. The publishers claim that the probability that a randomly chosen child who completes a…

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Question 7 · 8 marks · Continuous random variables (probability density functions)

The diagram shows the graph of the probability density function, f, of a random variable X which takes values between 0 and 4 only. Between these two values the graph is a…

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