Uber rating approximation

Uber drivers are rated on a scale of 1 - 5, whole integers only. Cumulative rating is based upon rolling average of last 500 ratings. Curve is skewed. For example, with a rating of 4.80, 89% of ratings are 5's; with a 4.86, 92%.

WITHOUT KNOWING the specific rating(s) that are dropping off and given a desired average rating on the next t trips, can a statistical approximation of the change in cumulative rating be determined?

For example: given a cum rating of 4.85, how many consecutive 5's are needed to raise the rating to 4.86? Algorithm (Alegbra I) yields 33.33 trips but a single trip could result in a .008 change (rating of 1 drops and is replaced by a 5, or vv). I am looking for a statistical solution where one could provide a margin of error for a specified confidence level.

I had statistics a LONG time ago & remember virtually nothing (I do remember mean,mode,average, concepts of standard dev. normal vs skewed curve, confidence level and margin of error)

Full algorithm available. pls reply email midwood57ccny61@gmail