AS & A Level Mathematics (9709) — May–June 2023, 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 · 6 marks · The Poisson distribution (Poisson approximation to the binomial)

In a certain country, 20540 adults out of a population of 6012300 have a degree in medicine. Use an approximating distribution to calculate the probability that, in a random…

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Question 2 · 8 marks · Continuous random variables (probability density functions)

The graph of the function f is a straight line segment from (0, 0) to (2, 1). (On the diagram, f(x) is plotted against x, with the value 1 marked on the f(x) axis and the values…

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Question 3 · 6 marks · Hypothesis tests (test for a population mean using a large sample)

In the past, the annual amount of wheat produced per farm by a large number of similar sized farms in a certain region had mean 24.0 tonnes and standard deviation 5.2 tonnes. Last…

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Question 4 · 6 marks · Sampling and estimation (confidence interval for a population mean)

A certain train journey takes place every day throughout the year. The time taken, in minutes, for the journey is normally distributed with variance 11.2. The mean time for a…

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Question 5 · 7 marks · The normal distribution (linear combinations of independent normal variables)

Large packets of rice are packed in cartons, each containing 20 randomly chosen packets. The masses of these packets are normally distributed with mean 1010 g and standard…

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Question 6 · 3 marks · Sampling and estimation (unbiased estimate of population variance)

A sample of 5 randomly selected values of a variable X is as follows: 1 2 6 1 a where a 0. Given that an unbiased estimate of the variance of X calculated from this sample is…

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Question 7 · 14 marks · Hypothesis tests (Poisson distribution)

The number of accidents per week at a certain factory has a Poisson distribution. In the past the mean has been 1.9 accidents per week. Last year, the manager gave all his…

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