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Statistical inference — Question 17

QCAA 2025, Paper 2 · 5 marks

Q17 · 2025 · Technology-activeComplex unfamiliar5 marks

QUESTION 17 (5 marks)

A variable, XX, is assumed to be normally distributed with μ=24.311\mu=24.311 and σ=5.102\sigma=5.102. Two 90% confidence intervals for μ\mu were calculated from two different random samples from XX, with the second sample being smaller than the first sample by 60. Both confidence intervals were calculated using the population standard deviation rather than their respective sample standard deviations. The confidence interval produced from the first sample was (23.560,25.498)(23.560,25.498). Determine the probability that the confidence interval produced from the second sample overlaps the confidence interval from the first sample.
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