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Question: An ambulance station, 30 miles from one end of a 100-mile road, services accidents along the whole road. Suppose accidents occur with uniform distribution along the road, and the ambulance can travel at 60 miles an hour. Let T minutes be the response time (between when accident occurs and when ambulance arrives).

Find P(T > 30).

b) Find P(T > t) as a function of t. Sketch its graph.

c) Calculate the density function of T.

d) Calculate the mean and standard deviation of T.

e) What would be a better place for the station? Explain.

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