Linear combinations of random variables: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 6.1 Linear combinations of random variables, 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 20 questions on Linear combinations of random variables, as a list

June 2025, Statistics Major, Q2 (8 marks): At a toy factory, wooden blocks of approximate heights 20 mm, 30 mm and 50 mm are made in red, yellow and green respectively. The heights of the blocks in mm ar
June 2024, Statistics Major, Q3 (8 marks): At a launderette the process of cleaning a load of clothes consists of three stages: washing, drying and folding. The times in minutes for each process are mode
June 2024, Statistics Major, Q10 (9 marks): Ben takes an underground train to work and back home each day. The waiting time is defined as the time from when he reaches the station platform until he boards
June 2023, Statistics Major, Q4 (11 marks): A machine manufactures batches of 100 titanium sheets. The thickness of every sheet in a batch is Normally distributed with mean n mm and standard deviation 0.0
June 2023, Statistics Minor, Q3 (10 marks): A fair four-sided dice has its faces numbered 0, 1, 2, 3. The dice is rolled three times. The discrete random variable X is the sum of the lowest and highest sc
June 2023, AS Statistics A, Q3 (7 marks): At a pottery which manufactures mugs, it is known that 5% of mugs are faulty. The mugs are produced in batches of 20. Faults are modelled as occurring randomly
June 2022, Statistics Major, Q2 (7 marks): A manufacturer is testing how long coloured LED lights will last before the battery runs out, using two different battery types. The times in hours before the b
June 2022, AS Statistics B, Q6 (9 marks): The length L of a particular type of fence panel is Normally distributed with mean 179.2 cm and standard deviation 0.8 cm. You should assume that the lengths of
November 2021, Statistics Major, Q5 (17 marks): A manufacturer uses three types of capacitor in a particular electronic device. The capacitances, measured in suitable units, are modelled by independent Normal
November 2021, Statistics Major, Q9 (6 marks): The discrete random variable X has a uniform distribution over the set of all integers between -n and n inclusive, where n is a positive integer. 1 (a) Given th
November 2021, Statistics Major, Q10 (9 marks): Sarah takes a bus to work each weekday morning and returns each evening. The times in minutes that she has to wait for the bus in the morning and evening are mo
November 2021, AS Statistics B, Q2 (10 marks): Natasha is investigating binomial distributions. She constructs the spreadsheet in Fig. 2 which shows the first 3 and last 4 rows of a simulation involving two
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, Q3 (8 marks): A supermarket sells cashew nuts in three different sizes of bag: small, medium and large. The weights in grams of the nuts in each type of bag are modelled by i
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, Q3 (9 marks): The weights of bananas sold by a supermarket are modelled by a Normal distribution with mean 205 g and standard deviation 11 g. (a) Find the probability that th
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, Q6 (7 marks): The discrete random variable X has a uniform distribution over { , n n 1 , ..., 2 n } . + 3 (a) Given that n is odd, find ( P X 1 n ) . [1] 2 3 (b) Given instea
June 2019, AS Statistics B, Q3 (9 marks): A bus runs from point A on the outskirts of a city, stops at point B outside the rail station, and continues to point C in the city centre. The journey times fo
June 2018, AS Statistics B, Q2 (9 marks): A supermarket sells oranges. Their weights are modelled by the random variable X which has a Normal distribution with mean 345 grams and standard deviation 15 g

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