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.