Inference using normal and t-distributions: past paper questions

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• Question 3May/June 2026, paper 41Structured6 marks

  Students studying geography at a college choose either human geography or physical geography. A teacher is investigating the times taken by students to complete assignments of equal difficulty in human geography and physical geography.

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• Question 1Oct/Nov 2025, paper 41Structured6 marks

  A group of 10 school children are asked to estimate the size of an angle ${\theta }^{\circ }$ in a given acute angled triangle.

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• Question 1Oct/Nov 2024, paper 41Structured6 marks

  Ellie is investigating the heights of two types of beech tree, $A$ and $B$, in a certain region.

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• Question 1Oct/Nov 2023, paper 41Structured6 marks

  Maya is an athlete who competes in 1500-metre races. Last summer her practice run times had mean 4.22 minutes. Over the winter she has done some intense training to try to improve her times.

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• Question 5May/June 2026, paper 41Structured8 marks

  Margaret has developed a new revision course to help students improve their ability in mathematics. The students each sit a mathematics test before attending the course and a test of similar difficulty after attending the course.

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• Question 3Oct/Nov 2025, paper 41Structured4 marks

  A random sample of 10 newborn baby boys is taken and their masses in kg are recorded. From this sample, the population standard deviation of all newborn baby boys is estimated as 0.6 kg.

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• Question 6Oct/Nov 2024, paper 41Structured8 marks

  Ansal is investigating the wingspans of Monarch butterflies in two different regions, $X$ and $Y$. He takes a random sample of 8 Monarch butterflies from region $X$ and records their wingspans, $x\text{ cm}$. His results are as follows.

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• Question 3Oct/Nov 2023, paper 41Structured8 marks

  Scientists are studying the effects of exercise on LDL blood cholesterol levels. Over a three-month period, a large group of people exercised for 20 minutes each day.

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• Question 6Oct/Nov 2025, paper 41Structured9 marks

  Nine athletes in a club have a new coach. The coach adopts a new training programme which he believes will reduce the race times of these athletes. Each athlete completes a 1500 m time trial before and after completing the new training programme.

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• Question 1Oct/Nov 2024, paper 42Structured4 marks

  A scientist is investigating the lengths of the leaves of a certain type of plant. The scientist assumes that the lengths of the leaves of this type of plant are normally distributed.

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• Question 1Oct/Nov 2023, paper 42Structured6 marks

  A factory produces small bottles of natural spring water. Two different machines, $X$ and $Y$, are used to fill empty bottles with the water. A quality control engineer checks the volumes of water in the bottles filled by each of the machines.

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• Question 2Oct/Nov 2025, paper 42Structured7 marks

  A factory produces packets of biscuits. The total mass of biscuits in a packet has a normal distribution with mean $\mu$. A random sample of 12 packets is taken and the mass of the contents of each packet, $x\text{ g}$, is recorded.

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• Question 5Oct/Nov 2024, paper 42Structured9 marks

  Dev owns a small company which produces bottles of juice. He uses two machines, $X$ and $Y$, to fill empty bottles with juice. Dev is investigating the volumes of juice in the bottles.

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• Question 5Oct/Nov 2023, paper 42Structured16 marks

  A company is deciding which of two machines, $X$ and $Y$, can make a certain type of electrical component more quickly.

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• Question 1May/June 2026, paper 43Structured6 marks

  A random sample of 9 observations of a normally distributed random variable $X$ is as follows. $$\begin{array}{ccccccccc}19.4& 21.3& 24.0& 20.7& 18.9& 21.2& 22.5& 23.4& 20.8\end{array}$$ The population mean of $X$ is $\mu$.

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• Question 5Oct/Nov 2025, paper 42Structured9 marks

  An engineer is comparing the tensile strengths of steel rods made from two machines, $A$ and $B$. The engineer randomly selects 8 rods from machine $A$ and 6 rods from machine $B$. The tensile strengths, in appropriate units, are given in the following table.

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• Question 5May/June 2026, paper 43Structured11 marks

  Rhiannon is investigating the mass of individual bananas sold in two supermarkets. Rhiannon claims that the mean mass of bananas sold by supermarket $X$ is less than the mean mass of bananas sold by supermarket $Y$.

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• Question 1May/June 2024, paper 41Structured4 marks

  The times taken by members of a large cycling club to complete a cross-country circuit have a normal distribution with mean $\mu$ minutes.

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• Question 1May/June 2023, paper 41Structured4 marks

  The lengths of the leaves of a particular type of tree are normally distributed with mean $\mu \text{ cm}$. The lengths, $x\text{ cm}$, of a random sample of 12 leaves of this type are recorded. The results are summarised as follows.

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• Question 6May/June 2024, paper 41Structured8 marks

  Jade is a swimming instructor at a sports college. She claims that, as a result of an intensive training course, the mean time taken by students to swim 50 metres has reduced by more than 1 second. She chooses a random sample of 10 students.

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• Question 2May/June 2023, paper 41Structured8 marks

  The children at two large schools, $P$ and $Q$, are all given the same puzzle to solve.

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• Question 1May/June 2025, paper 41Structured7 marks

  The manager of a hardware store is interested in whether there is a difference in the amount spent per customer on weekdays ($x)comparedtoweekends($y).

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• Question 4May/June 2025, paper 41Structured7 marks

  A researcher is interested in whether there is a difference between two schools in students' aptitude for English. She randomly chooses 10 students from school $X$ and 8 students of a similar age from school $Y$ to take a written English test.

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• Question 2May/June 2024, paper 43Structured7 marks

  A rowing club has a large number of members. A random sample of 12 of these members is taken and the pulse rate, $x$ beats per minute (bpm), of each is measured after a 30-minute training session.

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• Question 2May/June 2023, paper 43Structured6 marks

  Shane is studying the lengths of the tails of male red kangaroos. He takes a random sample of 14 male red kangaroos and measures the length of the tail, $x\mathrm{m}$, for each kangaroo.

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• Question 4May/June 2025, paper 42Structured7 marks

  A researcher is interested in whether there is a difference between two schools in students’ aptitude for English. She randomly chooses 10 students from school $X$ and 8 students of a similar age from school $Y$ to take a written English test.

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• Question 6May/June 2024, paper 43Structured10 marks

  Seva is investigating the lengths of the tails of adult wallabies in two regions of Australia, $X$ and $Y$. He chooses a random sample of 50 adult wallabies from region $X$ and records the lengths, $x\text{ cm}$, of their tails.

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• Question 4May/June 2023, paper 43Structured9 marks

  An inspector is checking the lengths of metal rods produced by two machines, $X$ and $Y$. These rods should be of the same length, but the inspector suspects that those made by machine $X$ are shorter, on average, than those made by machine $Y$.

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• Question 2May/June 2025, paper 43Structured7 marks

  A farmer is investigating whether using a new fertiliser will increase the yield of tomato plants. The farmer selects 40 tomato plants at random and gives them the new fertiliser. The crop mass, $x\text{ kg}$, of each of these 40 plants is recorded.

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