When a randomly selected number A is rounded off to the nearest integer Rᴀ, it is reasonable to assume that the round-off error A- Rᴀ is uniformly distributed on the interval (-.5,.5).
If 50 numbers are rounded off to the nearest integer and then averaged, approximate the probability that the resulting average differs from the exact average of the 50 numbers by more than 0.1 (round your answer to 4 digits).