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

a.

Number of accidents occurred in 100,000 days = 5230

Number of days in 2 weeks = 2 * 7 = 14

Average number of accidents every two weeks = (5230/100,000) * 14 = 0.7322

So, the estimated number of accidents in a 2-week period if the traffic light were to be installed is 0.7322

b.

The rate of accidents at the intersection is about one every two weeks before traffic light installation = 1

The estimated number of accidents in a 2-week period if the traffic light were to be installed is 0.7322

As, the estimated number of accidents in a 2-week period if the traffic light were to be installed is less than the rate of accidents at the intersection every two weeks before the installation, the simulation show that adding the traffic light would be a good idea.

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