An intersection has a four-way stop sign but no traffic light. Currently, about

Question

An intersection has a four-way stop sign but no traffic light. Currently, about 1200 cars use the intersection a day, and the rate of accidents at the intersection is about one every two weeks. The potential benefit of adding a traffic light was studied using a computer simulation by model- ing traffic flow at the intersection if a light were to be installed. The simulation included 100,000 repetitions of 1200 cars using the intersection to mimic 100,000 days of use. Of the 100,000 sim- ulations, an accident occurred in 5230 of them, and no accident occurred in the rest. (There were no simulated days with two or more accidents.) a. Based on the results of the simulation, what is the estimated number of accidents in a 2-week period if the traffic light were to be installed? b. Does the simulation show that adding the traffic light would be a good idea? Explain

Explanation / Answer

With traffic lights,

Number of accidents in 100,000 days = 5230

Number of accidents in a day = 5230/100000 = 0.0523

This follows a poisson distribution which has an average of 0.0523

Number of accidents in 2 weeks is 14*0.0523 ie.0.7322.

1 accident over 2 week period.

b)

number of accident without lights is one for 2 weeks

number of accidents/ day is 1/14 i.e 0.07143

This rate is higher than the one with traffic lights.

Hence it warrants having traffic lights.

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