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We present a numerical study of the soliton formation in a standard single mode fiber pumped by pulses in pico- and sub nano-second range of duration in presence of normally distributed noise. We took into the account modulation instability, self and cross phase shift, self frequency shift in the nonlinear Schrödinger equation. The sequence of pulses originated from the pulse was studied. The power of the first soliton and the distance at which its time delay reaches 3 times of the pulse duration were calculated. Then the soliton power and the distance were averaged and the standard deviation was calculated. For pulses with duration of 50 ps and longer the pulse breakup starts from the amplification of the noisy modulation of the pulse amplitude by modulation instability mechanism even for very low noise power. For pulses shorter than 10 ps the wave breakup starts from the pulse collapse with standard deviation equals to 0 for any experimentally reasonable noise power. For intermediate pulse duration wave breakup starts from the pulse collapse at low noise power, while for higher noise power modulation instability prevails. We have found some surprising feature in the 50-ps long pulses behaviour that shows slower development of solitons at higher noise power. These numeric results are in enough agreement with experimental results, which an optical pulse of 300 ps and width 5 nm, broaden to 100 nm, its phenomenon is namely supercontinuum. [ABSTRACT FROM AUTHOR]