Sampling distributions and the central limit theorem: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 7.1 Sampling distributions and the central limit theorem, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 19 questions on Sampling distributions and the central limit theorem, as a list

June 2025, AS Statistics A, Q1 (3 marks): A student is investigating what level of exercise is given to dogs in the UK by their owners. (a) When trying to collect suitable information, give two reasons
June 2024, Statistics Major, Q5 (10 marks): A researcher is investigating whether doing yoga has any effect on quality of sleep in older people. The researcher selects a random sample of 40 older people,
June 2024, Statistics Major, Q11 (11 marks): The discrete random variable X has a uniform distribution over the set of all integers between 25 and n inclusive, where n is a positive integer with n 2 25 . J
June 2023, Statistics Major, Q8 (12 marks): The random variable X has a continuous uniform distribution over [0, 10]. (a) Find the probability that, if two independent values of X are taken, one is less t
June 2023, Statistics Minor, Q2 (5 marks): A company manufactures batches of twenty thousand tins which are subsequently filled with fruit. The company tests tins from each batch to make sure that they a
June 2022, Statistics Major, Q9 (11 marks): The random variable X has a discrete uniform distribution over the values {0, 1, 2, …, 20}. (a) Find P(X G 7). [1] (b) Find each of the following. • E(X) • Var(
June 2022, AS Statistics B, Q3 (8 marks): A local council collects domestic kitchen waste for composting. Householders place their kitchen waste in a ‘compost bin’ and this is emptied weekly by the coun
November 2021, Statistics Major, Q1 (6 marks): When babies are born, their head circumferences are measured. A random sample of 50 newborn female babies is selected. The sample mean head circumference is 34.
November 2021, Statistics Major, Q11 (11 marks): The continuous random variable X has probability density function given by Z ] 2 ax 0 x 2 , 1 G ] 2 f ( ) x b ( 3 x ) 2 x 3 , [ = - G G ]] 0 otherwise , \ where
November 2021, AS Statistics B, Q5 (9 marks): A food company makes mini apple pies. The weight of pastry in a pie is Normally distributed with mean 75 g and standard deviation 4 g. The weight of filling in
November 2020, Statistics Major, Q4 (6 marks): An amateur meteorologist records the total rainfall at her home each day using a traditional rain gauge. This means that she has to go out each day at 9 am to r
November 2020, Statistics Major, Q8 (10 marks): In this question you must show detailed reasoning. On the manufacturer’s website, it is claimed that the average daily electricity consumption of a particular m
November 2020, Statistics Major, Q10 (12 marks): The discrete random variables X and Y have distributions as follows: X + B(20, 0.3) and Y + Po(3). The spreadsheet in Fig. 10 shows a simulation of the distribu
June 2019, Statistics Major, Q7 (11 marks): A swimming coach believes that times recorded by people using stopwatches are on average 0.2 seconds faster than those recorded by an electronic timing system.
June 2019, Statistics Major, Q9 (15 marks): Every weekday Jonathan takes an underground train to work. On any weekday the time in minutes that he has to wait at the station for a train is modelled by the
June 2019, Statistics Minor, Q3 (4 marks): A company has been commissioned to make 50 very expensive titanium components. A sample of the components needs to be tested to ensure that they are sufficientl
June 2019, AS Statistics B, Q1 (6 marks): It is known that the red blood cell count of adults in a particular country, measured in suitable units, has mean 4.96 and variance 0.15. (a) Find the probabili
June 2018, AS Statistics B, Q4 (15 marks): The random variable X has a continuous uniform distribution on [0, 10]. ^ h. (i) Find P X [1] 3 1 1 6 (ii) Find each of the following. • E(X) • Var(X) [2] Maris
June 2018, AS Statistics B, Q6 (10 marks): A company has a large fleet of cars. It is claimed that use of a fuel additive will reduce fuel consumption. In order to test this claim a researcher at the com

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