A structure determined by X-ray crystallography has a resolution of 1.5 Å. When I look at the coordinates, I find every backbone C-N distance is 1.32 Å.i.e. Accurately predicted. If resolution is not good why every C-N bond distance is accurately predicted?
The structural model of a protein is obtained using both experimental data and prior knowledge about geometry of macromolecules. As a structural model is refined, interatomic distances are also restrained. So, the C-N distance isn't really predicted. Alternatively, knowledge about this distance is used to construct reasonable model.
In response to the comment below I'll cite Rupp's Biomolecular Crystallography, the most comprehensive book on this subject. Refinement and restraints are covered in Chapter 12, Model building and refinement.
An observation does not have to be an experimental observation (measured data) specific to the particular structure, but can be any type of general prior knowledge regarding molecular stereochemistry. Known stereochemistry can be exploited and implemented in macromolecular refinement in the form of geometric constraints and restraints. [...]
We know from accurate and precise small molecule and peptide fragment structures [...] that bond lengths and bond angles show distinct and relatively narrow distributions around their mean positions. [...]
Refinement programs read restraint target values specific for each residue and each ligand molecule from restraint library files, which are subject to continuous empirical update.
The value given in this book (Table 12-1) for peptide bond C-N is 1.336 Å with variance 0.023 Å.