In this Coursera lecture by Mercedes Paniccia on inelastic scattering of electrons off hadrons, at 1:45 she says that
At moderate $q^2$, inelastic processes produce excited states of the nucleon, also called resonances, such as $\Delta^+$, which have the same quantum numbers as the proton. These resonances have an extremely short lifetime and therefore a broad mass distribution.
I assume that the broad mass distribution means that the invariant mass of the produced resonance can assume values over a broad range. Why does the resonance lifetime being short imply that its mass distribution is broad?