A transportation engineer wishes to design a left turn lane at a highway intersection. the cars turning left arrive at this intersection following a...

A transportation engineer wishes to design a left turn lane at a highway intersection. the cars turning left arrive at this intersection following a Poisson distribution. If the cycle time of the traffic light (for left turns) is 1 minute, and the design criterion requires a left turn lane that will be sufficient 90% of the time, what should be the lane length (in car lengths) to allow an average of 150 left turns per hour? What is the probability distribution of the left turn inter-arrival times?