80 



BINOMIAL AND NORMAL DISTRIBUTIONS 



Ch. 4 



This figure also can be described as the graph of the binomial fre- 

 quency distribution when n = 10 and p = 1/2. 



It is apparent that the actual form of a binomial frequency dis- 

 tribution depends upon two numbers, n and p. If p = 1/2 = 1 — p, 



Figure 4.12/1. 



3 4 5 6 7 



Number of occurrences (r) 

 (p=2/9) 



10 



Graph of the binomial frequency distribution with p = 2/9 and 

 n= 10. 



30 



2 20 - 



3 4 5 6 7 



Number of occurrences (r) 

 (P = 13/16) 



10 



Figure 4.12B. Graph of the binomial frequency distribution with p = 13/16 and 



n= 10. 



the graph is symmetrical, as in Figure 4.11. If p > 1/2, the event £/ 

 is more likely to occur than to fail to occur; hence the higher ordinates 

 of the graph will be toward the right-hand side of the graph. If 

 p < 1/2, the reverse situation is expected. These remarks are illus- 

 trated in Figures 4.12A and B. For Figure 4.12A, p = 2/9; and for 

 Figure 4.125, p = 13/16. In both cases n = 10. The series for the 

 binomials (7/9 + 2/9) 10 and (3/16 4- 13/16) 10 were employed in the 



