Mathematics — Probability · law-of-large-numbers-continuous
Problem
(a) Suppose a number X is chosen at random from [0,20] with uniform probability. Find a lower bound for the probability that X lies between 8 and 12, using Chebyshev's Inequality.
(b) Now suppose 20 real numbers are chosen independently from [0,20] with uniform probability. Find a lower bound for the probability that their average lies between 8 and 12.
(c) Now suppose 100 real numbers are chosen independently from [0,20]. Find a lower bound for the probability that their average lies between 8 and 12.