For X ~ N(120, 15²) and n = 9, compute the SE and the two probabilities about X̄: above 128, and between 115 and 125.

Answer

import math def phi(z): return 0.5 * (1 + math.erf(z / math.sqrt(2))) mu, sigma, n = 120, 15, 9 se = sigma / math.sqrt(n) above = 1 - phi((128 - mu) / se) between = phi((125 - mu) / se) - phi((115 - mu) / se) print(f"SE={se:.1f} P(Xbar>128)={above:.4f} P(115<Xbar<125)={between:.4f}")

H-W7 (the explicit statement and small-n examples) — shape only; IBS1 §7.1 (the general result), CC BY 4.0; original dataset