In this paper we study numerically an ensemble of one-parameter maps driven by fractal noises. There are two accessible cases of on-off intermittency in the system for different values of parameters. The first one, corresponding to the loss of stability of the fixed point, has a power law laminar phase distribution of exponent H-2, while the second one, due to the instability of the synchronous motion of the ensemble, has a distribution depending on the form of the map. A simple analysis of the mechanism of this difference is also given. The distribution for the case far from the critical state is reported.