A key aspect of culture is the definition of acceptable behavior. The culture defines the minimum acceptable behavior. This does not preclude groups or individuals within the culture from exceeding the bar.
Actions deemed below the bar can have consequences (e.g. in a sample corporate culture swearing in a meeting might be below acceptable and result in some form of chastisment).
Setting the bar
Cultural norms can be defined by laws or just developed contextually within organizational constraints, or a combination. Within organizational culture leaders have marked influence on what is acceptable.
While leaders provide direction the members of the organization forge the details. These can be clearly documented or could just be experiential.
That is to say, developed through actual group behaviors and practices over time, or a combination of influences together with clearly documented rules and associated consequences.
Some organizations use comprehensive clearly documented policies strictly to guide and enforce culture well others are more elemental in their approaches. Those cultures just develop over time, in whatever direction.
Striving for Excellence
If the members of your organization are are not stretching to go beyond the cultural bar of what constitutes acceptable, don’t expect more than mediocre results overall.
And if the team is striving to just reach the minimum acceptable level, that probably means the culture acknowledges that low quality is okay (it meets the definition of acceptable) then maybe it’s time to think about changing team members.
Is this the kind of performance you really want?