The optical dielectric function for a bundle of aligned single-wall carbon nanotubes (SWCNs) with randomly distributed diameters has been calculated in the one-electron approximation. It is shown that the superposition of the spectral lines corresponding to the interband transitions in SWCNs of different sizes results in a strong broadening, intensity decrease, and red (respectively, blue) shift of the resonant peak in the spectrum of the real (respectively, imaginary) part of the response function. The implication of the findings for understanding the optical properties of realistic SWCN samples is discussed.