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Radiated noise from gearbox housings is a significant contributor to the noise, vibration, and harshness (NVH) performance of automotive drivetrains. Small deviations in wall thickness caused by standard manufacturing tolerances can influence structural stiffness, shift modal frequencies, and alter acoustic radiation levels, particularly near resonance. This study numerically examines the effect of ±10% wall thickness variation using a simplified multi-mode structural–acoustic model. Modal frequencies were scaled proportionally to thickness changes, and frequency response functions were calculated for nominal and tolerance-limit geometries. Statistical variability was assessed through Monte Carlo simulations with wall thickness values sampled from a truncated normal distribution within the tolerance range. Results show that a ±10% variation can produce modal frequency shifts accompanied by resonance amplitude differences of up to 20.9 dB in the 950–1050 Hz range, with an average change of 3.34 dB between extreme cases. Monte Carlo analysis indicated mean changes of 0.54 dB in the main resonance band, with some cases reaching 2.54 dB. The findings demonstrate that even within standard production limits, wall thickness tolerances can measurably affect gearbox NVH behavior. Considering such variability in early-stage design can help reduce unit-to-unit noise differences and improve acoustic robustness.