In the PRINCE2 customer/supplier environment, it is typically the customer's responsibility to specify the desired result of the project. This responsibility involves defining what the project should achieve in terms of outcomes and benefits, aligning with the customer's business objectives. References: PRINCE2 Foundation official study materials.

Quality assurance is responsible for carrying out independent audits within a project. These audits are designed to ensure that the project complies with external standards and internal policies at an organizational level, distinct from the project-focused activities. References: PRINCE2Foundation Training Manual; PRINCE22017 Foundation handbook.

Qualitative analysis of a risk in PRINCE2 assesses, at a minimum, the likelihood of each risk occurring and its potential impact on project objectives. This analysis helps in prioritizing risks based on their severity and likelihood, which is crucial for effective risk management and decision-making about risk responses.
References: (PRINCE27 Foundation Handbook, AXELOS)

The Closing a Project process in PRINCE2 is triggered towards the end of the final stage when all assigned work has been completed. This process is designed to ensure that all project objectives have been achieved, all products have been delivered, and the project can be formally closed and evaluated for success and areas of improvement. References: PRINCE2 Foundation manual, PRINCE2 official resources

The purpose of the Directing a Project process in PRINCE2 is to enable the Project Board to exercise overall control over the project while delegating day-to-day management of the project stages to the Project Manager.
This ensures that the Project Board can make key decisions and remain accountable for the project's success while not being involved in the lower-level, day-to-day activities. References: PRINCE2 Foundation manual, PRINCE2 official resources