90 lUil.I. SVSTF.M rnCHKICAL JOlRX.Il. 



hour is roughly proportional to tin- aiiinunt of iralitic. haiullrd. Tlu- 

 results of these tests arc summarized in such a manner as to show the 

 percentage of tests which are not answered within 5, 10 and 20 seconds. 

 The traffic man who gives this matter thought, is concerned to know 

 how much reliance he can place on the results of these tests as being 

 representati%e of the percentage of slow answers appK^ing to all the 

 calls handled in the office. 



The speculative traffic man 1)\- this time is in a frame of mind 

 which either leads him to tlouht all figures or to feel that there must 

 he something in the figures which he cannot explain hut which makes 

 certain of them quite representative, although there are certain 

 others about which he does not feel the same way. He is sure that 

 some of them are representative because decisions and programs 

 based on them produce the results desired. He is also sure that 

 some of them are not representative because they imply things which 

 he knows are not so, as a result of observation. Just how far he can 

 rely upon the figures which he is using, and where to draw the line 

 is a question which only long experience or an understanding of the 

 reasons which lie behind the taking of these records can solve. It 

 will probabK' be of interest to discuss, from the purely theoretical 

 angle, certain simple traffic data with the idea of noticing how the 

 application of a certain mathematical ]iroce(lurc- can aid in drawing 

 accurate conclusions from them. 



The tN'iic of traffic prohleni which will lie consiiitTcd ma\' be slated 

 as follows: 



A groui) of .')(),()()() calls originated in an exchange area. An unknown 

 number of iJuin were deia>x'd more than 10 seconds. ()l)siT\a- 

 tions were made on 'MK) of the calls and of these 9, or 3 per cent., were 

 dela\ed more than 10 seconds. With this information is it a safe bet 

 that the unknown percentage for the entire 50,000 calls is below o? 

 Or better yet, are we justified in betting !)9 in 100 that the unknown 

 percentage for the .")(), 000 calls is below 5? Or again, nia\- we bet 

 8 in 10 that the unknown percentage is between ().') ami .').^ It is 

 taken for granted that the obser\er is justified in belie\ing that the 

 calls under consideration fulfill the conditions -of ranilom siimpling 

 such as that each call is independent of e\ery other call, or that an 

 appreciable ntnuber of the calls is not due to the occurrence of some 

 unusual e\enl,- the opi-ning of the first game of the wcirld series, 

 for exami)le. 



Assuming that the reader is unfamiliar with the theory of proba- 

 bility, a digression becomes necessary and in order that he inay enter 

 into the s()iril of the tiieory the reader is re<iuested to forget for the 



