The ability of new instruments for providing accurate inferences of vector magnetic fields and line-of-sight velocities of the solar plasma depends a great deal on the sensitivity to these physical quantities of the spectral lines chosen to be measured. Recently, doubts have been raised about visible Stokes profiles to provide a clear distinction between weak fields and strong ones filling a small fraction of the observed area. The goal of this paper is to give qualitative and quantitative arguments that help in settling the debate since several instruments that employ visible lines are either operating or planned for the near future. The sensitivity of the Stokes profiles is calculated through the response functions (RFs), for e.g., by Ruiz Cobo & Del Toro Iniesta. Both theoretical and empirical evidences are gathered in favor of the reliability of visible Stokes profiles. The RFs are also used for estimating the uncertainties in the physical quantities due to noise in observations. A useful formula has been derived that takes into account the measurement technique (number of polarization measurements, polarimetric efficiencies, and number of wavelength samples), the model assumptions (number of free parameters and the filling factor), and the radiative transfer (RFs). We conclude that a scenario with a weak magnetic field can reasonably be distinguished with visible lines from another with a strong field but a similar Stokes V amplitude, provided that the Milne-Eddington approximation is good enough to describe the solar atmosphere and the polarization signal is at least 3 or 4 times larger than the typical rms noise of 10-3 I c reached in the observations.