Question

Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate of 51 per minute during the 5:00 to 6:00 p.m. hour (assume Exponential distribution). If an auto has just arrived, what is the probability: a) That the next auto will arrive within 3 seconds? b) That the next auto will arrive in the next 3 to 10 seconds? c) That the next auto will arrive after 2 seconds?

Answer 1

a) P ( arrival time < 0.05 ) = 1 - e^-(51)(0.05) = 0.922

b) P (0.05< arrival time <0.167 ) = e^-(51)(0.05) - e^-(51)(0.167) = 0.0779

c) P ( arrival time > 0.033 ) = e^-(51)(0.033) = 0.186