Air carrier Captain reported the First Officer descended below glidepath on a visual approach and they received a low altitude alert from ATC.

Narrative

SKC; excellent visibility; light winds; MTV 1. When arriving at ZZZ landing north; TRACON vectored us to a very short final at an altitude higher than optimum. As the PM; I became distracted by 'cleaning up' the FMS for the approach; assuming the PF would be able to manage the short vector. The PF descended below glidepath approximately 5 miles from the field; resulting in a 'low altitude' alert from ATC. Since we were on a visual approach with no obstacles affecting our route; we elected to continue the approach as we were not unstable; and continuing the approach appeared to be a safe course of action.Failure by the CA (PM) to properly monitor the FO (PF) during the visual approach to ZZZ; which was made mildly difficult by ATC giving us a short vector to final. CA was biased toward assuming the FO would be able to manage the approach. This bias occurred due to the CA making assumptions about the FO's skill level when considering the FO's background. CA should not become distracted during critical phases of flight. In the future; I will be more diligent about monitoring the PF during the final approach phase. Honestly; I'm embarrassed that I let this happen. As I put my head down to work on the FMS; I assumed that we were going to have the opposite problem: high and fast at the FAF; so I was preparing to manage that situation.