If we pick 20 random numbers from the [0..1] by means of a random number generator with any distribution, e.g. with python numpy.random.random(20), then the probability that the average of the sample (20 numbers) would deviate by more than 1/4 from the theoretical mean equal is less 0.16.
In our case t=1/4, n=20, if we use the uniform distribution of picking numbers then E(Sn)=1/2, hence Pr( | Sn – 1/2 | ≥ 1/4) ≤ 0.16 .
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