Determination of Normal Curve from Tail 



25 



TABLE XI. Constants of Normal Curve from Moments of Tail 



about Stump. 



Values of the Functions -v^, and ^, 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 ^ from ^ = S'/d*. Hence from table determine h'. 



(ii) From this value of h' find >/r 2 , then o-=dxi|r 2 gives the standard 

 deviation of the uncurtailed normal curve. 



(iii) h = h'x(T gives the origin of the uncurtailed normal curve. 



(iv) Knowing h', Table II gives | (1 + a) and therefore the ratio £(1 — a) 

 of tail to total area of curve JV, or JV = nj% (1 - a). For many purposes it is 

 sufficient to use N — nx yjr,. 



