Sampling Distribution Tool
See how x̄ behaves: standard error, the CLT normal curve, and P(a < x̄ < b).
Example: μ = 100, σ = 15, n = 36 — what’s P(97 < x̄ < 103)?
① Answer
② Steps
③ Why it works
The Central Limit Theorem: sample means x̄ are less variable than individuals — their spread shrinks by √n: SE = σ/√n. And for large n, x̄ is approximately normal around μ no matter the population’s shape. Bigger samples don’t change the center — they just concentrate the curve.