Central limit theorem for the modulus of continuity of averages of observables on transversal families of piecewise expanding unimodal maps

We prove that the Newton quotient of the average R(t) of a lipschitzian function (with non vanishing variation) with respect to the SRB measure on a transversal family f_t of piecewise expanding unimodal maps, after an appropriated normalization, converges in distribution to the normal distribution.