Binomial distributions can be approximated by a normal distributions if the expected number of observations is large enough.
All samples have the same frequency distribution.
None realy, except that the observations must be independent. Although the above procedure is the one generally found in text-books, it is not the best one. This approach is an approximation, even with the continuity correction. The Chi-square distribution can only be used if all expected values, i.e., all Eij , are larger than five . If this does not hold, combine the rarer categories with larger ones.