For a skewed days-to-pay population with μ = 38, σ = 12 and n = 36, compute the SE and the two CLT probabilities: x̄ above 41, and x̄ between 36 and 42.

Answer

import math def phi(z): return 0.5 * (1 + math.erf(z / math.sqrt(2))) mu, sigma, n = 38, 12, 36 se = sigma / math.sqrt(n) above = 1 - phi((41 - mu) / se) between = phi((42 - mu) / se) - phi((36 - mu) / se) print(f"SE={se:.1f} P(Xbar>41)={above:.4f} P(36<Xbar<42)={between:.4f}")

H-W7 (statement and condition) — shape only; IBS1 §7.1–7.2 (the simulations), IS1 §7.3, CC BY 4.0; original dataset