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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 ,
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

(4.79) 
each contribution
having a distribution which satisfies
the conditions of the central limit theorem.
Giulio D'Agostini
20030515