assumptions made for a normal distribution- a interview question I was asked in my interview:
What assumptions can you make? Why and when? (i.e When is it safe to assume "normal"). 
Can some one answer this . 
 A: You can make any assumptions you like. Then you have to support them or show that they are not (grossly) violated or show that methods that don't use those biases give similar results.
For example, we can assume the errors from a ordinary least squares regression are normally distributed (note that OLS regression makes additional assumptions, e.g. independence and homoskedasticity).  We can then show evidence that they are, indeed, normal by looking at the residuals of the model in various ways (e.g. quantile normal plots, tests of normality, examination of skew and kurtosis). In addition, we can use robust regression on the same variables and see if the results are very different from the ones in OLS (e.g. by looking at the parameter estimates or by comparing the predicted values).  
Or, we can assume that the relationship between x and y is linear and test that by looking at scatter plots or by adding a quadratic term to the model and seeing what it does or by using splines and seeing how "unstraight" they are. 
