We present a general phenomenological model for the metallicity distribution (MD) in terms of [Fe/H] for dwarf spheroidal galaxies (dSphs). These galaxies appear to have stopped accreting gas from the intergalactic medium and are fossilized systems with their stars undergoing slow internal evolution. For a wide variety of infall histories of unprocessed baryonic matter to feed star formation, most of the observed MDs can be well described by our model. The key requirement is that the fraction of the gas mass lost by supernova-driven outflows is close to unity. This model also predicts a relationship between the total stellar mass and the mean metallicity for dSphs in accord with properties of their dark matter halos. The model further predicts as a natural consequence that the abundance ratios [E/Fe] for elements such as O, Mg, and Si decrease for stellar populations at the higher end of the [Fe/H] range in a dSph. We show that, for infall rates far below the net rate of gas loss to star formation and outflows, the MD in our model is very sharply peaked at one [Fe/H] value, similar to what is observed in most globular clusters. This result suggests that globular clusters may be end members of the same family as dSphs.
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