Final answer:
The coordinator of the quality group is demonstrating legitimate power by inviting the CNL to join, as it is rooted in the accepted authority of the coordinator's organizational role.
Step-by-step explanation:
In the scenario described, the coordinator of the quality group inviting the clinical nurse leader (CNL) to join the group is demonstrating legitimate power. This type of power, according to sociologist Max Weber's classification, is rooted in accepted structural positions within an organization or a system, and is associated with a person's role or position. In this case, the inherent authority of the coordinator's position gives them the right to invite new members into the quality improvement committee. Legitimate power is supported by the rules and regulations of the institution and is recognized as a rightful form of authority by members of the organization.