Correction for known systematic errors

It is easy to be convinced that if our prior knowledge about $Z$ was of the kind

$$Z\sim {\cal N}(z_\circ,\sigma_Z)$$ (5.70)

the result would have been

$$\mu \sim {\cal N}\left(x_1-z_\circ, \sqrt{\sigma_1^2+\sigma_Z^2}\right)\,,$$ (5.71)

i.e. one has first to correct the result for the best value of the systematic error and then include in the global uncertainty a term due to imperfect knowledge about it. This is a well-known and practised procedure, although there are still people who confuse $z_\circ$ with its uncertainty.