<p>The existing Cramer-Rao inequality under classical statistics applies only when all observations in the data are exact. Therefore, the existing Cramer-Rao inequality has the limitation of not utilizing the degree of uncertainty in the evaluation of the minimum variance estimator or in computing the amount of information. In this paper, we modify the existing Cramer-Rao inequality under neutrosophic statistics. The proposed Cramer-Rao inequality can utilize the degree of uncertainty and is applicable in the presence of imprecise data. We present some applications of the proposed Cramer-Rao inequality and conduct extensive computational study to assess the effect of the degree of uncertainty on the minimum variance. From the study, we conclude that the degree of uncertainty should be given attention when applying the Cramer-Rao inequality in practice.</p>