The proportion of responses to a question and its options, known as the response distribution, enables detailed analysis of human society. Recent studies highlight the use of Large Language Models (LLMs) for predicting response distributions as a cost-effective survey method. However, the reliability of these predictions remains unclear. LLMs often generate answers by blindly following instructions rather than applying rational reasoning based on pretraining-acquired knowledge. This study investigates whether LLMs can rationally estimate distributions when presented with explanations of “artificially generated distributions” that are against commonsense. Specifically, we assess whether LLMs recognize counterintuitive explanations and adjust their predictions or simply follow these inconsistent explanations. Results indicate that smaller or less human-optimized LLMs tend to follow explanations uncritically, while larger or more optimized models are better at resisting counterintuitive explanations by leveraging their pretraining-acquired knowledge. These findings shed light on factors influencing distribution prediction performance in LLMs and are crucial for developing reliable distribution predictions using language models.