The ability to explain the prediction of deep learning models to end-users is an important feature to leverage the power of artificial intelligence (AI) for the medical decision-making process, which is usually considered non-transparent and challenging to comprehend. In this paper, we apply state-of-the-art eXplainable artificial intelligence (XAI) methods to explain the prediction of the black-box AI models in the thyroid nodule diagnosis application. We propose new statistic-based XAI methods, namely Kernel Density Estimation and Density map, to explain the case of no nodule detected. XAI methods' performances are considered under a qualitative and quantitative comparison as feedback to improve the data quality and the model performance. Finally, we survey to assess doctors' and patients' trust in XAI explanations of the model's decisions on thyroid nodule images.