plumiEstimation, confidence intervals and tests: Edexcel A‑Level Further Maths questions
Every Edexcel 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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All 35 questions on Estimation, confidence intervals and tests, as a list
- June 2025, Further Statistics 2, Q3 (6 marks): A scientist investigated the effects of nitrogen-fixing bacteria on cereal crop yield, x kg ha –1 The data come from independent random samples from normal dist
- June 2025, Further Statistics 2, Q4 (13 marks): The weights of apples Sam grows are normally distributed with a mean of 131 g and a standard deviation of 6 g A supermarket will only buy apples with weights in
- June 2025, Further Statistics 2, Q6 (17 marks): Xiang owns a takeaway restaurant and wants to employ a delivery company. Xiang uses two companies, A and B, for one week each and records the delivery rate, x m
- June 2025, Further Statistics 2, Q7 (11 marks): A random sample X1 , X2 , X3 , X4 and X5 is taken from a distribution X ~ N (μ, σ 2) Nina and Jonah each use unbiased estimators to estimate μ Nina uses X‾ = 1
- June 2024, Further Statistics 1, Q4 (12 marks): Every morning Geethaka repeatedly rolls a fair, six‑sided die until he rolls a 3 and then he stops. The random variable X represents the number of times he roll
- June 2024, Further Statistics 2, Q3 (8 marks): A factory produces bolts. The lengths of the bolts are normally distributed with mean μ mm and standard deviation 0.868 mm A random sample of 15 of these bolts
- June 2024, Further Statistics 2, Q6 (12 marks): A researcher set up a trial to assess the effect that a food supplement has on the increase in weight of Herdwick lambs. The researcher randomly selected 8 sets
- June 2024, Further Statistics 2, Q7 (11 marks): Two organisations are each asked to carry out a survey to find out the proportion, p, of the population that would vote for a particular political party. The fi
- June 2023, Further Statistics 1, Q4 (6 marks): There are 32 students in a class. Each student rolls a fair die repeatedly, stopping when their total number of sixes is 4 Each student records the total number
- June 2023, Further Statistics 1, Q5 (8 marks): A machine fills cartons with juice. The amount of juice in a carton is normally distributed with mean µ ml and standard deviation 8 ml. A manager wants to test
- June 2023, Further Statistics 2, Q2 (12 marks): Camilo grows two types of apple, green apples and red apples. The standard deviation of the weights of green apples is known to be 3.5 grams. A random sample of
- June 2023, Further Statistics 2, Q3 (8 marks): Two machines, A and B, are used to fill bottles of water. The amount of water dispensed by each machine is normally distributed. Samples are taken from each mac
- June 2023, Further Statistics 2, Q5 (9 marks): A psychologist claims to have developed a technique to improve a person’s memory. A random sample of 8 people are each given the same list of words to memorise
- June 2023, Further Statistics 2, Q8 (12 marks): A bag contains a large number of marbles of which an unknown proportion, p, is yellow. Three random samples of size n are taken, and the number of yellow marble
- June 2022, Further Statistics 1, Q5 (5 marks): A random sample of 150 observations is taken from a geometric distribution with parameter 0.3 Estimate the probability that the mean of the sample is less than
- June 2022, Further Statistics 1, Q7 (11 marks): A machine fills bags with flour. The weight of flour delivered by the machine into a bag, X grams, is normally distributed with mean μ grams and standard deviat
- June 2022, Further Statistics 2, Q2 (12 marks): A factory produces yellow tennis balls and white tennis balls. Independent samples, one of yellow tennis balls and one of white tennis balls, are taken. The tab
- June 2022, Further Statistics 2, Q4 (8 marks): A doctor believes that a four-week exercise programme can reduce the resting heart rate of her patients. She takes a random sample of 7 patients and records the
- June 2022, Further Statistics 2, Q5 (8 marks): The concentration of an air pollutant is measured in micrograms/m3 Samples of air were taken at two different sites and the concentration of this particular air
- June 2022, Further Statistics 2, Q6 (15 marks): Korhan and Louise challenge each other to find an estimator for the mean, μ, of the continuous random variable X which has variance σ 2 X1, X2, X3, …, Xn are n
- November 2021, Further Statistics 1, Q3 (4 marks): A courier delivers parcels. The random variable X represents the number of parcels delivered successfully each day by the courier where X ~ B (400, 0.64) A rand
- November 2021, Further Statistics 1, Q7 (8 marks): A manufacturer has a machine that produces lollipop sticks. The length of a lollipop stick produced by the machine is normally distributed with unknown mean μ a
- November 2021, Further Statistics 2, Q2 (9 marks): A company produces two colours of candles, blue and white. The standard deviation of the burning times of the blue candles is 2.6 minutes and the standard devia
- November 2021, Further Statistics 2, Q5 (10 marks): The continuous random variable X is uniformly distributed over the interval [0, 4β ], where β is an unknown constant. Three independent observations, X1, X2 and
- November 2021, Further Statistics 2, Q6 (15 marks): Elsa is collecting information on the wingspan of two different species of butterfly, Ringlet and Meadow Brown. She takes a random sample of each type of butter
- November 2020, Further Statistics 1, Q7 (15 marks): A six-sided die has sides labelled 1, 2, 3, 4, 5 and 6 The random variable S represents the score when the die is rolled. Alicia rolls the die 45 times and the
- November 2020, Further Statistics 2, Q1 (6 marks): 1 Gina receives a large number of packages from two companies, A and B. She believes that the variance of the weights of packages from company A is greater than
- November 2020, Further Statistics 2, Q2 (6 marks): 2 Jemima makes jam to sell in a local shop. The jam is sold in jars and the weight of jam in a jar is normally distributed. Jemima takes a random sample of 8 of
- November 2020, Further Statistics 2, Q4 (7 marks): 4 A biased coin has a probability p of landing on heads, where 0 < p < 1 Simon spins the coin n times and the random variable X represents the number of heads.
- November 2020, Further Statistics 2, Q6 (12 marks): 6 A new employee, Kim, joins an existing employee, Jiang, to work in the quality control department of a company producing steel rods. Each day a random sample
- June 2019, Further Statistics 1, Q3 (6 marks): A biased spinner can land on the numbers 1, 2, 3, 4 or 5 with the following probabilities. Number on spinner 1 2 3 4 5 Probability 0.3 0.1 0.2 0.1 0.3 The spinn
- June 2019, Further Statistics 2, Q1 (8 marks): 1 A machine is set to fill pots with yoghurt such that the mean weight of yoghurt in a pot is 505 grams. To check that the machine is working properly, a random
- June 2019, Further Statistics 2, Q3 (8 marks): 3 Yin grows two varieties of potato, plant A and plant B. A random sample of each variety of potato is taken and the yield, x kg, produced by each plant is meas
- June 2019, Further Statistics 2, Q5 (7 marks): 5 Alexa believes that students are equally likely to achieve the same percentage score on each of two tests, paper I and paper II. She randomly selects 8 studen
- June 2019, Further Statistics 2, Q6 (9 marks): 6 A company manufactures bolts. The diameter of the bolts follows a normal distribution with a mean diameter of 5 mm. Stan believes that the mean diameter of th
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