  Summation arithmetic functions of Mertens and Liouville are investigated in
the paper. It is proved that the limiting distribution of these functions is
the normal. It is also shown that the estimating of standard deviation of these
functions $O(n^{1/2})$ cannot be improved. The estimate of the average of
Liouville summation function is found. The estimate of the order of growth of
the ratio of the summation functions of Mertens and Liouville is also found.
