The origin of the observed large peculiar motion (almost-equal-to 600 km s-1) of the Local Group (we adopt a mean expansion H0 = 100 km s-1 Mpc-1) is still in question. Recently, several candidates (large concentrations of matter) have been suggested to explain this deviation from the Hubble flow. On the other hand, different studies have revealed the existence of vast empty regions. We use a model in which the universe contains clusters with mass excess delta-M and voids with mass deficiency -delta-M. By considering a determinate distribution of these two types of structures, we can estimate the microwave background radiation fluctuations due to the gravitational effects created by the inhomogeneities. We use the recent upper limit on the smoothed sky autocovariance function (Davies et al. 1987) and the bound on the quadrupole anisotropy (Strukov & Skulachev 1988) to obtain information about the maximum number density of structures of the type dominating the local deviation from the Hubble flow. By considering a Poisson spatial distribution of these structures at z less than or similar to 10(3), we estimate the probability of finding one of them in our surroundings. We find that the standard candidate (Lynden-Bell et al. 1988; Dressler 1988) for the Great Attractor is not very typical (probability less than or similar to 10-30%). The probability of finding an attractor at a distance of almost-equal-to 140 h-1 Mpc is < 10%. However, if we consider that matter is forming random ly-distributed cluster-void aggregates (i.e., aggregates constituted by a cluster and a void that are very close one to another), in general, we cannot obtain bounds on the probability of finding a determinate attractor in our surroundings.