  In this paper we prove that in the high temperature region of the
Sherrington-Kirkpatrick model for a typical realization of the disorder the
weighted average of spins $\sum_{i\leq N} t_i \sigma_i$ will be approximately
Gaussian provided that $\max_{i\leq N}|t_i|/\sum_{i\leq N} t_i^2$ is small.
