Standard Normal CDF

Notes:

• This is one of the most important function in Statistics. You encounter it whenever you work with the normal probability model. You also often use it when approximate calculation of probabilities are required.
• Geometrically, the integral in the above definition gives the area under the standard normal density to the left of point u. Since it is a cdf, it follows that
  
  
• The integral defining this cdf cannot be evaluated in closed form, i.e., it cannot be expressed in terms of elementary functions. Therefore, to obtain values of this function you need to use a statistical table (e.g., see Table 5) or appropriate computer software.
• Since the standard normal density is symmetric about zero, it follows that Statistical tables like Table 5 tend to exploit the symmetry mentioned above to limit tabulation of this function to positive-valued arguments. For negative-valued arguments, use the relationship just given to relate what you want to what is tabulated. For example, if Z has a standard normal distribution, then
  
  
  since, from Table 5,