identify differential size I.E, 8.8 or smaller or larger and gear ratio 4.11 or different

2003 navigator sat for 2 years roaring noise that starts at about 35 MPH and increases with acceleration goes away on decel below 35 MPH local mech says the ring and pinion are messed up local salvage yards say they have one but didn't ask about gear size or ratio does the vin list this