In fuzzy group decision making problems and fuzzy shortest path problems, the addition and subtraction are the basic problems. For the mixed normal fuzzy numbers and trapezoidal fuzzy numbers, the addition and subtraction operations are approximated by the normal fuzzy numbers in this paper. The behaviors of approximated normal fuzzy numbers are the same as those of the normal distributions from the viewpoint of probability. An application of the addition and subtraction operations of mixed fuzzy numbers to the fuzzy sample mean is also proposed.