Question: A number in the interval $[0, 4]$ is selected randomly. How many picks do you have to make so that the arithmetic mean $X$ satisfies $P[|X-2|\ge 0.1]\lt 0.01$ ?
Answer: I've solved by using Chebychev's theorem, to get $P[2-\frac{1}{10}\lt X\lt2+\frac{1}{10}]\ge 1-\frac{1}{10^2}$. Here we get $\mu=2, \sigma=\frac{1}{100}$. But I don't know how to continue to get the answer of "how many picks do you have to make so that..."