Concrete should achieve the strength as specified in your country codes or specifications.
Normally for normal grades of concrete here in India, almost everybody look for Characteristic + 4 Mpa up to some years back. Now the requirement is Characteristic + 3 Mpa.
We do target some strength base on assumptions of standard deviation and chances of failure in cubes 1 in 20 or whatever which gives the value of 'k'.
The trails we do with it always yield to more than what we targeted. So when we produce concrete in actual, it should not deviate by more than 4 Mpa from what we achieved in trials, if its deviating more than it, its an indication of something is wrong somewhere and you need to fix it.