Pierre Simon Laplace, Inverse Probability, Central Limit Theorem, Probability, Deep Dives.
when Z ~ N(0, 1) (Image by Author) Let’s substitute z_low and z_high in Eq. (2) with the corresponding formulae expressed in terms of Φ and α: (Image by Author) We know that Z_n is the standardized X_bar_n. So let’s substitute Z_n with the standardized X_bar_n: (Image by Author) Some simplification