Thank you, Jim.

Apologies for the ambiguous language. I have a measured probability (0.22) of success. The success of each trail corresponds to a particular weight (e.g., measured voltage 0.51 mV). This measurement has error (coefficient of variation + channel noise = 0.31). I am trying to calculate how 8 such units with similar successes and weights would behave (i.e, what is the expected mV and variance).

Here's what I did....
I have treated weight as a random normal variable such that:

weight_SD = RandomVariate[NormalDistribution[0.51,0.31], 100];

pTrials = RandomVariate[BinomialDistribution[8, 0.22], 100];

data = pTrials * weight_SD

Does this seem sound? Thanks again for the help :)