The 2x2x2 Rubik's cube has 3674160 possible configurations.  For 276 of those configurations, the optimal solve requires 14 quarter-turns.  (We consider that a half-turn counts as two quarter-turns.)

If I pick a random configuration out of the 3674160 possible configurations, what is the expected number of quarter-turns required to solve that configuration in the optimal way?  In other words, what is the average number of turns among the optimal solution of all possible configurations?

You can round your result to two decimal places.