The ejected mass distribution of type Ia supernovae directly probes progenitor evolutionary history and explosion mechanisms, with implications for their use as cosmological probes. Although the Chandrasekhar mass is a natural mass scale for the explosion of white dwarfs as type Ia supernovae, models allowing type Ia supernovae to explode at other masses have attracted much recent attention. Using an empirical relation between the ejected mass and the light curve width, we derive ejected masses $M_mathrm{ej}$ and $^{56}$Ni masses $M_mathrm{Ni}$ for a sample of 337 type Ia supernovae with redshifts $z < 0.7$ used in recent cosmological analyses. We use hierarchical Bayesian inference to reconstruct the joint $M_mathrm{ej}$-$M_mathrm{Ni}$ distribution, accounting for measurement errors. The inferred marginal distribution of $M_mathrm{ej}$ has a long tail towards sub-Chandrasekhar masses, but cuts off sharply above 1.4 $M_odot$. Our results imply that 25%-50% of normal type Ia supernovae are inconsistent with Chandrasekhar-mass explosions, with almost all of these being sub-Chandrasekhar-mass; super-Chandrasekhar-mass explosions make up no more than 1% of all spectroscopically normal type Ia supernovae. We interpret the type Ia supernova width-luminosity relation as an underlying relation between $M_mathrm{ej}$ and $M_mathrm{Ni}$, and show that the inferred relation is not naturally explained by the predictions of any single known explosion mechanism.
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