Inverse survival function giving x where the survival probability equals q
InverseSurvivalFunction[dist, q]
Plot[Table[InverseSurvivalFunction[BetaDistribution[1 / 2, β], q], {β, {1 / 4, 1 / 2, 1}}]//Evaluate, {q, 0, 1}, Filling -> Axis]
→ -Graphics-InverseSurvivalFunction[NormalDistribution[], 0.2]
→ 0.841621233572914InverseSurvivalFunction[WeibullDistribution[2, 5], 0.4]
→ 4.786153810404955