Very nice, Marco!
For this particular example (10^4 samples from a normal distribution with mean 1 and standard deviation 3 and z = 1.2) the FindDistribution approach results in a smaller root mean square error for the estimator of Pr(X < z) than the naïve count approach and is almost as good as knowing that the distribution is normal. Here are the root mean square errors I found using 1,000 simulations:
0.0041996 for the FindDistribution approach
0.0048878 for the naïve count approach
0.0039955 for the "knowing the distribution is normal but not the mean and standard deviation" approach.
Of course, depending on the distribution, the parameters of the distribution, the sample size, and the value of z, your mileage may vary.