std::normal_distribution(3)

NAME
std::normal_distribution - std::normal_distribution

Synopsis
   Defined in header <random>
   template< class RealType = double > (since C++11)
   class normal_distribution;
   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; μ,σ) =
   1
   σ
   √
   2π
   exp⎛
   ⎜
   ⎝
   -1
   2
   ⎛
   ⎜
   ⎝
   x-μ
   σ
   ⎞
   ⎟
   ⎠2
   ⎞
   ⎟
   ⎠
   Here \(\small\mu\)μ is the Mean and \(\small\sigma\)σ is the Standard deviation
   (stddev).
   std::normal_distribution satisfies all requirements of RandomNumberDistribution.

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.

Member types
   Member type Definition
   result_type (C++11) RealType
   param_type (C++11) the type of the parameter set, see RandomNumberDistribution.

Member functions
   constructor constructs new distribution
   (C++11) (public member function)
   reset resets the internal state of the distribution
   (C++11) (public member function)

Generation
   operator() generates the next random number in the distribution
   (C++11) (public member function)

Characteristics
   mean returns the distribution parameters
   stddev (public member function)
   (C++11)
   param gets or sets the distribution parameter object
   (C++11) (public member function)
   min returns the minimum potentially generated value
   (C++11) (public member function)
   max returns the maximum potentially generated value
   (C++11) (public member function)

Non-member functions
   operator==
   operator!= compares two distribution objects
   (C++11) (function)
   (C++11)(removed in C++20)
   operator<< performs stream input and output on pseudo-random number
   operator>> distribution
   (C++11) (function template)

Example
// Run this code
 #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::round(d(gen)); };
     std::map<int, int> hist{};
     for (int n = 0; n != 10000; ++n)
         ++hist[random_int()];
     for (auto [x, y] : hist)
         std::cout << std::setw(2) << x << ' ' << std::string(y / 200, '*') << '\n';
 }

Possible output:
 -2
 -1
  0
  1 *
  2 ***
  3 ******
  4 ********
  5 **********
  6 ********
  7 *****
  8 ***
  9 *
 10
 11
 12

External links
   1. Weisstein, Eric W. "Normal Distribution." From MathWorld — A Wolfram Web
       Resource.
   2. Normal distribution — From Wikipedia.