 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-iii/8/a/ii/solution

The sample mean is exactly

N (μ, σ^{2} / n)

, so

(\overline{X} - μ) / (σ / n)

0.95

to the interval

[- 1.96, 1.96]

. Inverting this pivot yields the exact

95%

[\overline{X} - 1.96 \frac{σ}{n}, \overline{X} + 1.96 \frac{σ}{n}] .

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