H2 Maths 6.3 - Normal Distribution: The Central Limit Theorem

What you will learn

• Sample of n observations from N(mu, sigma^2): X-bar has mean mu and variance sigma^2 / n exactly.
• Central Limit Theorem: for any parent distribution with mean mu and variance sigma^2, X-bar is approximately N(mu, sigma^2 / n) once n is large (typically n >= 30).
• Apples with E(X) = 150 and Var(X) = 100; n = 25 gives X-bar ~ N(150, 4) and P(X-bar > 152) = P(Z > 1) = 0.1587.