Standardise x = 138 for X ~ N(120, 15²), then un-standardise z = −0.8 back to a dollar amount.

Answer

mu, sigma = 120, 15 x = 138 z = (x - mu) / sigma z2 = -0.8 x2 = mu + z2 * sigma print(f"z({x})={z:.2f} x(z={z2})={x2:.1f}")

IBS1 §6.1 (the standard normal, z-scores), CC BY 4.0 — shape only; σ² notation per the course convention; original dataset