• Suppose a number [math]X[/math] is chosen at random from [math][0,20][/math] with uniform probability. Find a lower bound for the probability that [math]X[/math] lies between 8 and 12, using Chebyshev's Inequality.
• Now suppose 20 real numbers are chosen independently from [math][0,20][/math] with uniform probability. Find a lower bound for the probability that their average lies between 8 and 12.
• Now suppose 100 real numbers are chosen independently from [math][0,20][/math]. Find a lower bound for the probability that their average lies between 8 and 12.