Abstract: A Receiver Operating Characteristic (ROC) analysis of a power is important and useful in clinical trials. A Classical Conditional Power (CCP) is a probability of a classical rejection region given values of true treatment effect and interim result. For hypotheses and reversed hypotheses under normal models, we obtain analytical expressions of the ROC curves of the CCP, find optimal ROC curves of the CCP, investigate the superiority of the ROC curves of the CCP, calculate critical values of the False Positive Rate (FPR), True Positive Rate (TPR), and cutoff of the optimal CCP, and give go/no go decisions at the interim of the optimal CCP. In addition, extensive numerical experiments are carried out to exemplify our theoretical results. Finally, a real data example is performed to illustrate the go/no go decisions of the optimal CCP.