SOLUTION: Assuming that all numbers in a phone book are randomly selected. What would you expect the mean of the last four digits to be?

What do you mean by "the mean of the last four digits".
You could mean either: 

1. the expected average of all the four digit numbers made from
   the last four digits?  If so it would be the average of all
   the 4 digit numbers from 0000 to 9999, which would be the same
   as the median 4-digit, which is  
   There would on the average be as many 4 digit numbers above 
   the median 4-digit number 4999.5 as below it. 

or

2. the expected average of those last four digits averaged? 
   It would on the average be about the same as the average digit  
   That would be the median digit which is  
   for there would be on the average just as many digits above 
   the median digit 4.5 as there are below it. 

I'm guessing that you are asking for 2.  So I'd say the answer is 4.5.
But the question is a bit ambiguous, for I can't tell whether you are
asking for the average of all 4-digit numbers (counting numbers like
0000 and 0786 as 4-digit numbers) or the average of the 10 digits.  

Edwin