cumulative_normal_approx = function( z ){
  #
  # Returns:
  #   An approximatin to Phi(z) = 1-P(Z>=z) ~ pnorm(z) for the cumulative normal distribution.
  # 
  # See Page 157 from the book Probability and Statistics: For Engineering and the Sciences by Jay L. Devore
  #
  # Written by:
  # -- 
  # John L. Weatherwax                2009-04-21
  # 
  # email: wax@alum.mit.edu
  # 
  # Please send comments and especially bug reports to the
  # above email address.
  #
  #-----

  num = ( 83. * z + 351 ) * z + 562
  den = 703./z + 165
  0.5 * exp( -num/den )
  
}