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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.

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