SOME BIOLOGICAL PROBLEMS. 1 29 



and substitute w for 



217111 



then as a final form we have 



■j: 



2 C^ , 



Since the above expression is a well-known equation for the 

 probability integral, the degree of probability for any given limits 

 may be determined from the table. For computation we have 

 the following relation : 



2inn 

 — f~' 



(0 = 6 \ or d ^ CO \ 



\2inn \ 



and / = ip{(ii). 



As will be seen from the above relations, the degree of prob- 

 ability is proportional to the amount of deviation. Therefore in 

 any given case we can either increase or decrease the value of 

 probability by changing the value of the deviation. Thus in 

 order to facilitate a comparison of several sets of data, it would 

 be advantageous to fix the value of the probability and then 

 determine the corresponding amount of the deviation. If we take 

 0.75 for the value of the probability, it will be certainly high 

 enough for practical purposes. If we adopt this system, then the 

 corresponding value of co is fixed and is equal to 0.814. Thus 

 we do not even need to use the table to determine the amount of 

 deviation. If however one wishes to find any other value of the 

 probability than I have proposed {i. e., 0.75), such can be readily 

 obtained from the table. Thus the determination of the deviation 

 can be made by a simple arithmetical process. 



The following will illustrate a method of determination. Dr. 

 King has kindly supplied the data for this purpose and I wish to 

 thank her for that material. 



Example: Out of 1 6, loo tadpoles, 9,949 are examined. 5,136 

 are found to be females and 4,813 males. Find the probability 

 that the ratio of females to the entire lot lies between given limits. 



