How to Generate Gaussian Distribution for a given range say [0,100]

Question

Hello all,
Iam looking for a Gaussian Distribution for a given range say [0,100]. I dont have the mean or the standard Deviation. Also iam not that good at Statistics.
For this range [0,100] : the mean according to my knowledge should be : 50.
Now it is Standard Deviation : i dont have it but i dont want any negative values
I have got the following formula :
double val= Math.round(r.nextGaussian() * std + (range)/2);
where range is 100 which is obtained by subtracting the hi val - low val.
As i dont have std dev i cannot use the formula above.
My question is :
1. Can we get a normal/gaussian distribution for a given range, say [0,100] without specifying standard deviation. Is there any formula for it.
Reg
Sankut

Answer 1

A Gaussian distribution cannot be bounded; as previously noted, if it is it's not Gaussian. However, you can effectively approximate bounds. A range of
mean +/- 4 standard deviations (SD)
will include 99.997% of all observations. If we set (mean - min) equal to 4 SD, it will include "all" low-side observations. So,
4 SD = (50 - 0)
1 SD = 12.5
The Java method provides a distribution with a mean of 0.0 and a SD of 1.0. The formula the OP posted can be used then to adjust its output to what is wanted:
number = Randon.nextGaussian() * 12.5 + 50;
As a test, I ran a sample of 1000 and got the following distribution:
VALUE     FREQUENCY
<5     0
6-15     1
16-25     21
26-35     90
36-45     222
46-55     341
56-65     220
66-75     84
76-85     19
86-95     2
95     0If 3 SD is used instead of 4 SD, the range will include 99.7% of all observations.