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VICSpecialist MathematicsQuick questions

Unit 4: Data analysis, probability and statistics

Quick questions on Sample mean and the central limit theorem: VCE Specialist Mathematics Unit 4

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is distribution?
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Since n=36n = 36 is reasonably large, by the central limit theorem
What is standardise for the probability?
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Convert Xˉ=53\bar{X} = 53 to a zz-score using the standard error:
What is q1?
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State the mean and standard error of Xˉ\bar{X} for μ=20\mu = 20, σ=4\sigma = 4, n=16n = 16. [2 marks]
What is q2?
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By what factor must nn increase to halve the standard error? [1 mark]
What is q3?
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State the central limit theorem in one sentence. [2 marks]

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