When a randomly selected number a is rounded off to its, Basic Statistics

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When a randomly selected number a is rounded off to its

Question: When a randomly selected number A is rounded off to its nearest integer R_A, it is reasonable to assume that the round-off error A - R_A is uniformly distributed in (-0.5, 0.5). 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.

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