Determination of Normal Curve from Tail 25 



TABLE XI. Constants of Normal Curve from Moments of Tail 



about Stump. 



Values of the Functions ^r, and ty t required to determine the Constants of a 

 Normal Frequency Distribution from the Moments of its Truncated Tail. 



Let d equal distance of centroid of tail from stump, 2 = standard deviation of 

 the tail about its mean, and n = its area. 



(i) Find ^r, from >Jr, = S*/d'. Hence from table determine h'. 



(ii) From this value of h' find i/r a , then o-=dx^ 2 gives the standard 

 deviation of the uncurtailed normal curve. 



(iii) A = A'x<r gives the origin of the uncurtailed normal curve. 



(iv) Knowing h', Table II gives J (1 + at) and therefore the ratio (! ) 

 of tail to total area of curve N, or N = n/(l-a.). For many purposes it is 

 sufficient to use N = n x tr t . 



