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Showing content from https://en.cppreference.com/w/cpp/language/../numeric/random/normal_distribution.html below:

std::normal_distribution - cppreference.com

template< class RealType = double > class normal_distribution;

(since C++11)

Generates random numbers according to the Normal (or Gaussian) random number distribution. It is defined as:

\(\small{f(x;\mu,\sigma)}=\frac{1}{\sigma\sqrt{2\pi} }\exp{(-\frac{1}{2}{(\frac{x-\mu}{\sigma})}^2)}\)f(x; Î¼,Ï) = expâ â â â â ââ â â 2 â â â

Here \(\small\mu\)Î¼ is the Mean and \(\small\sigma\)Ï is the Standard deviation (stddev).

std::normal_distribution satisfies all requirements of RandomNumberDistribution.

[edit] Template parameters RealType - The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double. [edit] Member types Member type Definition result_type (C++11) RealType param_type (C++11) the type of the parameter set, see RandomNumberDistribution. [edit] Member functions constructs new distribution
(public member function) [edit] resets the internal state of the distribution
(public member function) [edit] Generation generates the next random number in the distribution
(public member function) [edit] Characteristics returns the distribution parameters
(public member function) [edit] gets or sets the distribution parameter object
(public member function) [edit] returns the minimum potentially generated value
(public member function) [edit] returns the maximum potentially generated value
(public member function) [edit] [edit] Non-member functions [edit] Example

#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <string>
 
int main()
{
    std::random_device rd{};
    std::mt19937 gen{rd()};
 
    // Values near the mean are the most likely. Standard deviation
    // affects the dispersion of generated values from the mean.
    std::normal_distribution d{5.0, 2.0};
 
    // Draw a sample from the normal distribution and round it to an integer.
    auto random_int = [&d, &gen]{ return std::lround(d(gen)); };
 
    std::map<long, unsigned> histogram{};
    for (auto n{10000}; n; --n)
        ++histogram[random_int()];
 
    for (const auto [k, v] : histogram)
        std::cout << std::setw(2) << k << ' ' << std::string(v / 200, '*') << '\n';
}

Possible output:

-1
 0
 1 *
 2 ***
 3 *****
 4 ********
 5 *********
 6 *********
 7 ******
 8 ***
 9 *
10
11

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