code: def normal_cdf(x, mu=0, sigma=1):
      
      arg = (x - mu) / (sigma * numpy.sqrt(2))
      res = (1 + erf(arg)) / 2
      return res
docs: Cumulative Normal Distribution Function.
  
      :param x: scalar or array of real numbers.
      :type x: numpy.ndarray, float
  
      :param mu: Mean value. Default 0.
      :type mu: float, numpy.ndarray
  
      :param sigma: Standard deviation. Default 1.
      :type sigma: float
  
      :returns: An approximation of the cdf of the normal.
      :rtype: numpy.ndarray
  
      Note:
          CDF of the normal distribution is defined as
          \frac12 [1 + erf(\frac{x - \mu}{\sigma \sqrt{2}})], x \in \R
  
          Source: http://en.wikipedia.org/wiki/Normal_distribution