In this paper, the Bootstrap and Jackknife methods are stated and using these methods, entropy is estimated. Then the estimators based on Bootstrap and Jackknife are investigated in terms of bias and RMSE using simulation. The proposed estimators are compared with other entropy estimators by Monte Carlo simulation. Results show that the entropy estimators based on Bootstrap and Jackknife have a good performance as compared to the other estimators. Next, some tests of normality based on the proposed estimators are introduced and the power of these tests are compared with other tests.