This is a common mistake, but this is not the correct way to estimate the parameters of a probability distribution.
I'm not exactly sure what you are doing in the notebook. Are you trying to fit to the CDF or Survival function of the sum of two Gaussian distributions? If so, wouldn't the range of the points be between 0 and 1?
It doesn't matter either way. There are correct ways to estimate the parameters of a distribution from a set of samples. The function EstimateDistribution does this.
For example, here is how you define a Mixture Distribution of two Gaussians with different means, but the same variance:
MixtureDistribution[{1, 1}, {NormalDistribution[m1, v], NormalDistribution[m2, v]}]