A rezoning changes the zoning district of a property on the official map. Because it amends the law, it is a legislative decision: the elected governing body, a city or town council or a county commission, makes it, usually after the planning commission holds a hearing and recommends approval or denial.
Nobody publishes a reliable national approval rate, and one would mean little, because the odds swing with the place and the request. A change that matches the future land use map of the comprehensive plan, has staff support and draws little opposition is in a very different position from one that would put dense housing or commercial use where the plan calls for low density.
The factors that matter most are consistent across the country: consistency with the comprehensive plan, the planning staff's recommendation, the planning commission's vote, the reaction of neighbors at the hearings, and the scale of the change. Courts in many states also look unfavorably on a change that singles out one small parcel for special treatment, often called spot zoning.
The most useful number is local: how often this government's governing body has approved rezonings, and rezonings like yours, over recent years, and how many decisions that rests on. A rate built on a handful of cases says little; one built on dozens says a lot. In Charleston, South Carolina, for example, as elsewhere in the state, the planning commission recommends and the council decides.