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We derive a probability distribution, confidence intervals and statistics of the quality (Q) factor of an arbitrarily shaped mode-stirred reverberation chamber, based on ensemble distributions of an idealized random cavity field with assumed perfect stir efficiency. It is shown that Q exhibits a Fisher-Snedecor F-distribution whose degrees of freedom are governed by the number of simultaneously excited cavity modes per stir state. The most probable value of Q is shown to be between a fraction 2/9 and 1 of its mean value, and between a fraction 4/9 and 1 of its asymptotic mean (composite Q) value. The arithmetic mean value is found to exceed the values of most other theoretical metrics for centrality of Q. For a rectangular cavity, we retrieve the known asymptotic expression for Q in the limit of a highly overmoded regime.