Statistical inference — Question 14

QCAA 2025, Paper 1 · 5 marks

Q14 · 2025 · Technology-freeSimple familiar5 marks

QUESTION 14 (5 marks)

A factory produces cans of juice. Each can has a labelled volume of 500 mL.

The factory manager conducted a random sample of 100 cans to assess whether the labelled volume was being met satisfactorily in production. The mean volume of the sample was 498.9 mL with a sample standard deviation of 4.0 mL.

Based on this sample and using a

z

-value of 2, determine an approximate confidence interval for the population mean volume.

[3 marks]

Industry regulation requires that the mean volume must meet or exceed the labelled volume. Use your result from Question 14a) to state whether the current production meets the regulation. Justify your decision using mathematical reasoning.

[2 marks]

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Statistical inference — Question 14

QUESTION 14 (5 marks)

QCAA guide · typeset solution

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