Why is normal distribution most common? I just want to know why normal distribution is very common in literature ? Does normal distribution offer certain benefits over the other distribution or is it just a convention ? 
 A: Some arguments which are by no means exhaustive:


*

*As already mentioned  - CLT + additional theorems (e.g. delta method) let us compute asymptotic distributions of estimators and tests in many cases, when exact finite-sample results are unknown or very hard to obtain. 

*From my experience with data from natural/social science studies, normally distributed results actually appear quite often in so-called 'real life'. In some fields - take quality control for example - you often work with data that are already somehow averaged so it is natural to expect they will behave according to normal distribution - this is, again, thanks to CLT. 

*Although they require using some tables or numerical integration, calculations involving normal distribution are - for the most part - analytically feasible, compared to many other important families of distributions or more general situations where you don't make specific distributional assumption. This makes it easier to explain those methods (tests, models etc.), implement or apply them to real data. I also think this is one of reasons why normal distributions appear so predominantly in introductory textbooks.


For more detailed discussion, I recommend chapter 6.2.2 of those notes: www.public.iastate.edu/~mskaiser/stat601/booknotes.processfile.pdf 
