  We analyze recent cold-atom experiments on imbalanced Fermi systems using a
minimal model with a BCS-like superfluid phase coexisting with a normal phase.
This model is used to extract the T=0 pairing gap in the fully paired
superfluid state. The recently measured particle density profiles are in good
agreement with the theoretical predictions obtained from the universal
parameters from previous Quantum Monte Carlo calculations. We find that the T=0
pairing gap is greater than 0.4 times the Fermi energy $E_F$, with a preferred
value of $0.45 \pm 0.05$ $E_F$. The ratio of the pairing gap $\Delta$ to the
Fermi Energy $E_F$ is larger here than in any other system of strongly-paired
fermions in which individual pairs are unbound.
