Determination of Normal Curve from Tail 



25 



TABLE XI. Constants of Normal Curve from Moments of Tail 



about Stump. 



Values of the Functions yp-i and y^^ required to determine the Constants of a 

 Normal Frequency Distribution from the Moments of its Truncated Tail. 



h' 



fi 



H 



^^3 



h' 



^l 



^2 



^3 



0-00 



■571 



V2o3 



2-000 



1-1 



•734 



1-977 



7^371 



0-01 



•573 



1^259 



2-016 



IS 



•746 



2 



051 



8 •ego 



0-02 



•574 



r2G5 



2-032 



1-3 



•757 



2 



126 



10-331 



0-03 



•576 



1-271 



2-049 



l-k 



•767 



2 



202 



12-383 



0-04 



•578 



1-276 



2-066 



IS 



■777 



2 



280 



14-968 



0-05 



•580 



1-282 



2-083 



1-6 



•787 



2 



358 



18-248 



0-06 



•581 



r288 



2-100 



1-7 



•796 



2 



437 



22-439 



0-07 



•583 



1-294 



2-118 



1-8 



-804 



2 



517 



27-832 



0-os 



•585 



1-300 



2-136 



1-9 



•813 



2 



598 



34-823 



0-00 



•587 



1-305 



2-155 



2-0 



•820 



2 



679 



43-956 



0-1 



•588 



1^3U 



2-173 



2-1 



•828 



2 



762 



55-977 



0-2 



•605 



1^371 



2-377 



2-2 



•835 



2 



845 



71-925 



0-3 



•622 



1-432 



2-617 



2-3 



•842 



2 



929 



93-248 



0-4 



•638 



1-495 



2-902 



2-4 



•848 



3 



013 



121-988 



0-5 



•653 



1-560 



3-241 



2-5 



•854 



3 



098 



161-038 



0-6 



•668 



1-626 



3-646 



2-6 



•860 



3 



184 



214-537 



0-7 



•682 



1-693 



4-133 



2'7 



-866 



3 



270 



288-434 



OS 



•G96 



1-762 



4-720 



i-s 



-871 



3 



357 



391-374 



0-9 



•709 



1 -833 



5-433 



2-9 



-876 



3 



445 



535-963 



1-0 



•722 



1-904 



6-303 



3-0 



•880 



3 



532 



740-796 



1-1 



•734 



1-977 



7-371 



s-s 



•888 



3^969 



[4299-226] 



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

 the tail about its mean, and w = its area, 



(i) Find y^i from >|ri = S'/^^^- Hence from table determine h'. 



(ii) From this value of h' find -t^^, then a-=dx-^a gives the standard 

 deviation of the uncurtailed normal curve. 



(iii) h = h'xcr gives the origin of the uncurtailed normal curve. 



(iv) Knowing h', Table II gives -J (1 + a) and therefore the ratio ^(1 — «) 

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

 sufficient to use N = n x yjr^. 



