Normal distribution of measurement errors

The central limit theorem is also important to justify why in many cases the distribution followed by the measured values around their average is approximately normal. Often, in fact, the random experimental error $e$, which causes the fluctuations of the measured values around the unknown true value of the physical quantity, can be seen as an incoherent sum of smaller contributions $e_i$

$$e = \sum_i e_i\,,$$ (4.79)

each contribution having a distribution which satisfies the conditions of the central limit theorem.