Large language models (LLMs) have become indispensable for automated code generation, yet the quality and security of their outputs remain a critical concern. Existing studies predominantly concentrate on adversarial attacks or inherent flaws within the models. However, a more prevalent yet underexplored issue concerns how the quality of a benign but poorly formulated prompt affects the security of the generated code. To investigate this, we first propose an evaluation framework for prompt quality encompassing three key dimensions: goal clarity, information completeness, and logical consistency. Based on this framework, we construct and publicly release CWE-BENCH-PYTHON, a large-scale benchmark dataset containing tasks with prompts categorized into four distinct levels of normativity (L0-L3). Extensive experiments on multiple state-of-the-art LLMs reveal a clear correlation: as prompt normativity decreases, the likelihood of generating insecure code consistently and markedly increases. Furthermore, we demonstrate that advanced prompting techniques, such as Chain-of-Thought and Self-Correction, effectively mitigate the security risks introduced by low-quality prompts, substantially improving code safety. Our findings highlight that enhancing the quality of user prompts constitutes a critical and effective strategy for strengthening the security of AI-generated code.