Mathematics — Probability · law-of-large-numbers-continuous
Problem
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 X miles from Hangtown, where X is a random variable uniformly distributed over [0,100].
(a) Find a lower bound for the probability P(∣X−50∣≤10).
(b) Suppose that in one bad week, 20 trucks break down. Find a lower bound for the probability P(∣A20−50∣≤10), where A20 is the average of the distances from Hangtown at the time of breakdown.