Question 8.2.11: The Pilsdorff beer company runs a fleet of trucks along the 1......
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.
(a) 0
(b) 7/12
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