xxxvi Tables for Statisticians and Biometricians [III 



We are now in a position to find *fr : 



- - -00469,57351, 4 = - "00000,17489, 



,01 *A_ 2 - o.on_4 , - "05607,75592 x -99530,25160 



Lit 



= -05581,41358, 

 and -f = -55581,41358. 



Again : ^ = '3210,9583* for a* = 2-8178,4167, 



ir+ 



and since o- = 4-1874,1727, a- * = 1-3445,6222, 



**! 



= 1-9003,7636, 



S t = M, ri + ^ = -0081,5667. 



Thus 1 ^, representing the area-ratio from the far terminal of the curve 

 y = y oa ?o (1 - x) 80 up to the distance '08 beyond the mode, ='991,8433. The true 

 area-ratio = '991,8381, or we have an error of five units in the sixth decimal place. 



We shall often be less successful than this, although we obtain results accurate 



(28 



enough for practical purposes. Thus let us take # 20 (1 x) 80 dx/BC2l, 81). The 



J'20 



/20 

 ratio aP(l-af>das/B (21, 81) is -4603,98454. Hence we can solve the problem 



fl'OO r72 



if we find, not the above integral, but & 30 (1 xfdx= a;' 80 (lx') ZQ da;', 



J -28 J O'OO 



which gives for the required quantity the first 21 terms of the binomial ('72 + -28) 101 , 

 thus escaping the mode of the binomial, which is at the 28th or 29th term. We 

 find, since t = 20 : 



u t = j ("72)81 ( -28)2o = -01629,59807, 



Cl = -434,8180,372, 



xi = 1-72668,34840, a = 3'9710,4843, 

 i/r = -53623,52048, 



Ifl ^ = -4687,1524, 

 *i 



S t+1 = -03907,00400, 



r-28 

 or a; 20 (1 - a) 80 das/B (21, 81) = '9609,2996. 



Jo 



* By interpolation from the ten-figure Table II. 



