Pierre Simon Laplace, Inverse Probability, Central Limit Theorem, Probability, Deep Dives.
you wish to find [μ_low, μ_high] such that the there is a 95% chance that the mean of X will lie in this interval. We set α = 0.05. P(μ_low ≤ μ ≤ μ_high) = (1 — 0.05). P(μ_low ≤ μ ≤ u_high) = (1–0.05) can be split into two terms as follows: P(μ ≤ μ_high) — P(μ ≤ μ_low) = (1 — 0.025) — (0.025) You’d