After @Zulrah contacted me to help him with some data, I ran a function I made earlier to collect data to visualize the gRandom's output (using MethodProvider.gRandom(600, 200)). This is the image that I got using 10000 random calls:

The discription of the method says that it generates based on normal distribution, then this is is not what the graph should look like, right? Also the method says that it caps based on a secret maximum deviation. However I suspect something's going wrong there too, because every time I've run this function so far, the last value always has a count way higher than the previous ones. It's pretty much like all values above that cap are returned as the cap value, instead of just dismissing them which should be happening.

For the image above end results were: 

1197, 0
1198, 2
1199, 1
1200, 33

Image made using 15 million results by @Stimpack:

Edited March 28, 20179 yr by Reveance

Let me know if you like this better:

 

Random random = new Random();
int stdDeviation = 5;
int mean = 100;
for (int i = 0; i < 50; ++i) {
    double result = random.nextGaussian() * stdDeviation + mean;
    double max = mean + stdDeviation * 3; //68–95–99.7 rule
    if (result > max)
        result = max;
    System.out.println((int) Math.round(result));
}

48 minutes ago, Alek said:

Let me know if you like this better:

 

Random random = new Random();
int stdDeviation = 5;
int mean = 100;
for (int i = 0; i < 50; ++i) {
    double result = random.nextGaussian() * stdDeviation + mean;
    double max = mean + stdDeviation * 3; //68–95–99.7 rule
    if (result > max)
        result = max;
    System.out.println((int) Math.round(result));
}

That's actually great! Totally forgot to use that rule, however the only thing is that because you put result = max, if the value is above that range, essentially the 'tail numbers' of the ranges will get a high percentage again. Or in other words the chance of getting result == max is pretty high. Resulting in: 



I think the only way to prevent this is by re-generating the random so every value has a fair chance again:

Random random = new Random();
int stdDeviation = 5;
int mean = 100;
for (int i = 0; i < 50; ++i) {
	double maxOffset = stdDeviation * 3; //68–95–99.7 rule
	double result;
	do {
		result = random.nextGaussian() * stdDeviation + mean;
	} while (result > mean + maxOffset || result < mean - maxOffset); // Math.abs(result - mean) > maxOffset, don't know which'd be faster
}

Fair enough, final product looks something like this:

 

Random random = new Random();
int stdDeviation = 5;
int mean = 100;
double max = stdDeviation * 3; //68–95–99.7 rule
for (int i = 0; i < 50; ++i) {
    int result;
    do {
        result = Math.toIntExact(Math.round(random.nextGaussian() * stdDeviation + mean));
    } while (Math.abs(result - mean) > max);
}

Alright great