UNKNOWN MEAN OF SAMPLED UNIVERSE 645 



equidistant above and below x, lies the proportion of the total area 

 corresponding to the desired probability.^^ 



V. Conclusions 



We have presented a general equation for the probability that the 

 true mean of a sampled normal universe lies within a given ranger 

 incorporating the kind of knowledge the investigator m^y be expected 

 to have before the sample was made as well as the information directly 

 presented by the individual observations themselves. It cannot be 

 overemphasized that the problem by its very nature is indefinite 

 since it would be a rare instance indeed to find a mathematical expres- 

 sion which would completely and exactly summarize the a priori 

 knowledge, impressions and beliefs in the mind of any person con- 

 fronted with its solution. All that can be found is, at best, an approxi- 

 mate probability based upon certain assumptions we are willing to 

 make in order to arrive at a numerical result. And only by utilizing 

 as far as possible all of the available knowledge will the most nearly 

 correct probability values ascertainable be realized. 



11 On certain test cases of "Student " distributions, the error in planimeter readings 

 averaged about one-half of one per cent, and in no case exceeded one per cent. 



42 



