When a risk manager needs to prioritize resources to respond to multiple identified risks, qualitative analysis is the most appropriate tool. Qualitative analysis helps in evaluating the likelihood and impact of each risk using subjective criteria, allowing the risk manager to prioritize which risks require more immediate attention or resources based on their potential impact on the project.
PMI's guidelines on risk management suggest that qualitative analysis is particularly useful in the initial stages of risk assessment, where risks are categorized and ranked based on their severity. This process helps in prioritizing risks that need immediate attention, thus optimizing the use of resources in a project.