AS & A Level Mathematics (9709) — May–June 2024, Paper 61

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 · The Poisson distribution (sum of independent Poisson variables; P(X > 3))

A bus station has exactly four entrances. In the morning the numbers of passengers arriving at these entrances during a 10-second period have the independent distributions…

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Question 2 · 5 marks · The normal distribution (linear combinations of independent normal variables)

The random variable X has the distribution N(31.2, 10.4^2). Two independent random values of X, denoted by X1 and X2, are chosen. Find P(X1 3X2).

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Question 3 · 6 marks · Sampling and estimation (confidence interval for a population mean, known variance)

The time taken in minutes for a certain daily train journey has a normal distribution with standard deviation 5.8. For a random sample of 20 days the journey times were noted and…

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Question 4 · 9 marks · Sampling and estimation (unbiased estimates of population mean and variance)

A random sample of 8 boxes of cereal from a certain supplier was taken. Each box was weighed and the masses in grams were as follows. 261 249 259 252 255 256 258 254 Find unbiased…

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Question 5 · 8 marks · The Poisson distribution (conditions for a Poisson model)

Sales of cell phones at a certain shop occur singly, randomly and independently. State one further condition that must be satisfied for the number of sales in a certain time…

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Question 6 · 8 marks · Continuous random variables (probability density functions)

The diagram shows the graph of the probability density function, f, of a random variable X. The graph is a quarter circle entirely in the first quadrant with centre (0, 0) and…

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Question 7 · 11 marks · Hypothesis tests (test for a population proportion using the binomial distribution)

Every July, as part of a research project, Rita collects data about sightings of a particular kind of bird. Each day in July she notes whether she sees this kind of bird or not,…

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