Early and accurate prediction of endotracheal tube (ETT) location is pivotal for critically ill patients. Automatic and timely detection of faulty ETT locations from chest X-ray images may avert patients' morbidity and mortality. Therefore, we designed convolutional neural network (CNN)-based algorithms to evaluate ETT position appropriateness relative to four detected key points, including tracheal tube end, carina, and left/right clavicular heads on chest radiographs. We estimated distances from the tube end to tracheal carina and the midpoint of clavicular heads. A DenseNet121 encoder transformed images into embedding features, and a CNN-based decoder generated the probability distributions. Based on four sets of tube-to-carina distance-dependent parameters (i.e., (i) 30-70 mm, (ii) 30-60 mm, (iii) 20-60 mm, and (iv) 20-55 mm), corresponding models were generated, and their accuracy was evaluated through the predicted L1 distance to ground-truth coordinates. Based on tube-to-carina and tube-to-clavicle distances, the highest sensitivity, and specificity of 92.85% and 84.62% respectively, were revealed for 20-55 mm. This implies that tube-to-carina distance between 20 and 55 mm is optimal for an AI-based key point appropriateness detection system and is empirically comparable to physicians' consensus.