44 RELATIVE FREQUENCIES IN SIMPLE SAMPLING 
ability of death from pneumonia within a year of a per- 
son aged 30, it is more likely that we shall experience 5 
deaths than 7 deaths among the 10,000 exposed; for the 
probability 
Lig (£20) (55 ow 
5 J\5000) \5,000 
of 5 deaths is greater than the probability 
(150 Te 3 ) 
7 5,000 5,000 
of 7 deaths. 
Suppose we now set the problem of finding the prob- 
ability that upon repetition with another sample of 
10,000, the deviation from 6 deaths on either side will not 
exceed 3. The value to three significant figures calcu- 
lated from the binomial expansion is .854. To use the 
De Moivre-Laplace theorem, we simply make d=3 in 
(19), and obtain from tables of probability functions the 
value Py=.847. 
We should thus expect from the De Moivre-Laplace 
theorem a discrepancy either in defect more than 3 or in 
excess more than 3 in 100—84.7=15.3 per cent of the 
cases, and from the sum of the binomial terms we should 
expect such a discrepancy in 100—85.4 = 14.6 per cent of 
the cases. 
Turning next to tables of the Poisson exponential, 
page 122 of Tables for Statisticians and Biomelricians, we 
find that in 6.197 per cent of cases there will be a dis- 
crepancy in defect more than 3 and in 8.392 per cent of 
cases there will be a discrepancy in excess more than 3.