VCE Specialist Mathematics Past Exam Questions
Browse VCE Specialist Mathematics exam questions from 2015–2026, including NHT and VCE papers. Filter by topic, year and paper; open the original source.
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Section B, Question 6
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Estimated difficulty · Medium
Question 6 (9 marks) A manufacturer produces bottles of mineral water. The volume of mineral water in each bottle is normally distributed with a claimed population mean of 750 mL a
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE (NHT) Specialist Mathematics examination 2Section B, Question 6(a)Question part (a)
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Report-based difficulty · EasyAverage marks: 80% of available · official reportFull marks: 84% of students · official report
a. Find a 95% confidence interval for the population mean (the mean mass of all adult male koalas in the forest). Give your values correct to two decimal places. 1 mark
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a. For samples of 10 bottles, state the mean of the sampling distribution and show that the standard deviation of the sampling distribution is 10 5 mL. Assume that the mean volume
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Estimated difficulty · Easy
b. The inspectors will query the manufacturer’s claim that the mean volume of mineral water in all bottles produced is 750 mL if the mean volume in 10 randomly selected bottles is
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 58% of students · official report
b. Sixty such random samples are taken and their confidence intervals are calculated. In how many of these confidence intervals would the actual mean mass of all adult male koalas
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Estimated difficulty · Medium
i. What is the probability that the inspectors will query the manufacturer’s claim? Give your answer correct to four decimal places. Assume that the mean volume of mineral water in
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Estimated difficulty · Medium
ii. What is the probability that the inspectors will not query the manufacturer’s claim if the mean volume of mineral water in all bottles produced is in fact 749.5 mL and not the
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Report-based difficulty · DifficultAverage marks: 30% of available · official reportFull marks: 28% of students · official report
c. How many adult male koalas should be sampled to achieve this? 1 mark It is thought that the mean mass of adult male koalas in the forest is 12 kg. The ranger thinks that the tru
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Estimated difficulty · Medium
c. The graph shown below represents the sampling distribution of the mean for samples of 10 bottles, where the population mean is 750 mL and the standard deviation is 2 mL.
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i. On the axes below, for samples of 10 bottles, sketch the graph of the sampling distribution if the population mean is in fact 749.5 mL and the standard deviation is 2 mL. 1 mark
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ii. On the axes below, shade the area that represents the probability found in part b.ii. 1 mark 748 749 750 751 752 x The inspectors decide to apply a one-sided statistical test a
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Estimated difficulty · Easy
d. Write down suitable null and alternative hypotheses for this test. 1 mark 2023 SPECMATH EXAM 2 (NHT) 24 d o n o t w r i t e i n t h i s a r e a In applying the statistical test,
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE (NHT) Specialist Mathematics examination 2How to use ClassConnect past exam questions
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