The Pilsdorff beer company runs a fleet of trucks along the 100 mile road from Hangtown to Dry Gulch, and maintains a garage halfway in between. Each of the trucks is apt to break down at a point [math]X[/math] miles from Hangtown, where [math]X[/math] is a random variable uniformly distributed over [math][0,100][/math].

• Find a lower bound for the probability [math]P(|X - 50| \leq 10)[/math].
• Suppose that in one bad week, 20 trucks break down. Find a lower bound for the probability [math]P(|A_{20} - 50| \leq 10)[/math], where [math]A_{20}[/math] is the average of the distances from Hangtown at the time of breakdown.