Normal Distribution: Summary of Formulas 1.3 2008/06/06 14:49:07 GMT-5 2008/07/21 03:07:11.589 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics Normal Probability Distribution X ~ N ( μ , σ ) μ = the mean σ = the standard deviation Standard Normal Probability Distribution Z ~ N ( 0 , 1 ) Z = a standardized value (z-score)mean = 0 standard deviation = 1 Finding the kth Percentile To find the kth percentile when the z-score is known: k = μ + ( z ) σ z-score z = x - μ σ Finding the area to the left The area to the left: P ( X x ) Finding the area to the right The area to the right: P ( X x ) = 1 - P ( X x )