Normal Approximation to the Binomial

If

then, for sufficiently large n (and moderate p),

where

Notes:

• The above approximation is given without continuity correction. If you want an improved approximation, then consider using
  
  in place of the second expression displayed above. This is referred to as the normal approximation to the binomial with continuity correction. See the demonstration in IRIS for a numerical example and further discussion on this topic.
• The above normal approximation result is stated in a way which assumes that you are by now able to comfortably solve the important and basic problem of finding a cumulative normal probablity. Click the link just listed to find out how to solve such a problem if necessary.