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We exploit the knowledge of the entanglement spectrum in the ground state ofthe gapped XXZ spin chain to derive asymptotic exact results for the fullcounting statistics of the transverse magnetisation in a spin block of length.We found that for a subsystem of even length the full counting statistics isGaussian, while for odd subsystems it is the sum of two Gaussian distributions.We test our analytic predictions with accurate tensor networks simulations. Asa byproduct, we also obtain the symmetry (magnetisation) resolved entanglemententropies.

Full counting statistics in the gapped XXZ spin chain