plumiEstimation, confidence intervals and tests: OCR MEI A‑Level Further Maths questions
Every OCR MEI A-Level Further Maths exam question on FS.7 Estimation, confidence intervals and tests, 2018–2025, with its mark scheme and examiner’s report.
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![June 2023 Statistics Major, question 8: 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](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42201-jun23-08-qp.webp?v=3)
![June 2022 Statistics Major, question 9: 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(](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42201-jun22-09-qp.webp?v=3)
![November 2021 Statistics Major, question 11: 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](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y42201-nov21-11-qp.webp?v=3)
All 31 questions on Estimation, confidence intervals and tests, as a list
- June 2025, Statistics Major, Q3 (7 marks): Potatoes are sold in sacks of nominal weight 25 kg. As part of a trading standards check, a random sample of 50 sacks from a large batch is selected and softwar
- June 2025, Statistics Major, Q8 (13 marks): A teacher is investigating whether students run more quickly round an athletics track if they run in a clockwise direction rather than in an anti-clockwise dire
- 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, Q5 (13 marks): Amari is investigating how accurately people can estimate a short time period. He asks each of a random sample of 40 people to estimate a period of 20 seconds.
- 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, Q6 (11 marks): In this question you must show detailed reasoning. A particular type of skin cream is meant to contain an average of 12.2 g of liquid paraffin in a 200 g tub. 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, Q1 (10 marks): Each working day, Beth takes a bus to her place of work. She believes that the mean time that her journey takes is 30 minutes. In order to check this, Beth sele
- 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, Q7 (10 marks): A physiotherapist is investigating hand grip strength in adult women under 30 years old. She thinks that the grip strength of the dominant hand will be on avera
- 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, Q1 (9 marks): Over time LED light bulbs gradually lose brightness. For a particular type of LED bulb, it is known that the mean reduction in brightness after 10 000 hours is
- November 2021, AS Statistics B, Q3 (12 marks): The weights in kg of male otters in a large river system are known to be Normally distributed with mean 8.3 and standard deviation 1.8. A researcher believes th
- 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, Q7 (9 marks): The lengths in mm of a random sample of 6 one-year-old fish of a particular species are as follows. 271 293 306 287 264 290 (a) State an assumption required in
- 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, Q4 (7 marks): Shellfish in the sea near nuclear power stations are regularly monitored for levels of radioactivity. On a particular occasion, the levels of caesium-137 (a rad
- 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 2019, AS Statistics B, Q6 (11 marks): The label on a pack of strawberries in a large batch states that it holds 250 g of strawberries. A random sample of 40 packs from the batch is selected and soft
- June 2018, AS Statistics B, Q1 (6 marks): The birth weights, in kilograms, of a random sample of 9 captive-bred elephants are as follows. 94 138 130 118 146 165 82 115 69 A researcher uses software to p
- 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, Q5 (10 marks): The flight time between two airports is known to be Normally distributed with mean 3.75 hours and standard deviation 0.21 hours. A new airline starts flying the
- 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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