How to make numerically equal samples from the normal and any other distribution?

Question

Programming

Hi guys!
Given a set of instances, let's say a population of 1000 elephants. The elephant has a characteristic - weight. Its parameter is different for each elephant and has a normal distribution on the graph x^number_of_instances * y^weight. The average value of the parameter is 5000 kilograms.
Information about the distribution of weight in the population is given by six equal-width ranges.

1. 1000-2000 kg : 5 elephants
   
2. 2000-3000 kg : 15 elephants
   
3. 4000-5000 kg : 30 elephants
   
4. 6000-7000 kg : 30 elephants
   
5. 7000-8000 kg : 15 elephants
   
6. 8000+ kg: 5 elephants
   

The question is how to redefine the ranges of weights with some accuracy, based on the information above, in order to get five elephants (± one elephant) in each range. Ranges, respectively, will be more than six.
Ultimately, this needs to be programmed into a JS function, so if you can describe the problem not in mathematical, but in programming language, it will be even better.
I would be grateful for any hints that will push me in the right direction in finding a solution.

Answer 1

UPD. Since we have a normal distribution, we need to build a normal distribution estimated by the highest likelihood method.
And then calculate F ⁻¹ (0.05), F ⁻¹ (0.1), ..., F ⁻¹ (0.95).