The presence of noise in plasma particle measurements by scientific instruments causes inaccuracies in the determined plasma bulk parameters. This study demonstrates and evaluates the effects of noise in the determination of typical distribution functions describing the scattering angles of plasma particles passing through thin foils. First, we simulate measurements of plasma particles passing through a thin carbon foil, considering that their scattering angles follow kappa-like distribution functions, as being addressed in previous studies. We work with these specific distributions because we can produce them in the laboratory. We add Poisson-distributed background noise to the simulated data. We fit the simulated measurements and compare the fit parameters with the input parameters. As expected, we find that the discrepancy between the initial parameters and those derived from the fits increases with the relative increase of the noise. The misestimations exhibit characteristic trends as functions of the signal-to-noise ratio and the input parameters. Second, we examine the scattering angle distributions measured with a laboratory experiment of protons passing through a thin carbon foil for different signal-to-noise ratios. These measurements support the simulation results, although they exhibit a larger discrepancy than found in the simulations. Finally, we discuss how we can improve the accuracy of estimated distribution parameters in space and ground-based applications by excluding data-points from the tails of the distribution functions. Although our results exhibit the effects of noise in a specific type of distribution functions, we explain that this technique can be applied to and optimized for other specific data-sets.