Therefore, the choice of test of normality to be used should indisputable be given tremendous attention. This study focuses on comparing the power of four normality tests; SW, KS , AD and LF tests via Monte Carlo simulation. The simulation process was carried out using FORTRAN programming language. Section 2 discusses the classification of normality test. The Monte Carlo simulation methodology is explained in Section 3. Results and comparisons of the power of the normality tests are discussed in section 4. Finally a conclusion is given in Section 5.