Let x be the minimum probability of performance needed by each of the individual components 
    (x is the value under the problem's question).


Then the condition that the system performs properly is that each of the three
components works properly.


Since the components perform independently, this condition is 

    x^3 >= 0.92,

which gives

    x >=  = 0.972588826 (approximately),  or  0.9726  (rounded).   ANSWER