Pierre Simon Laplace, Inverse Probability, Central Limit Theorem, Probability, Deep Dives.
(Image by Author) Since the standard normal distribution is symmetrical around the Y-axis, z_low is simply the negative of z_high. Thus: The figure below illustrates the symmetry of the situation when α = 0.05, α/2 = 0.025, and (1 — α/2) = 0.975: Φ(z_low=-1.96) = 0.025, and Φ(z_high=1.96) = 0.975