Autos arrive at a toll plaza located at the entrance to a bridge at a rate of 50

Question

Autos arrive at a toll plaza located at the entrance to a bridge at a rate of 50 per minute during the 5:00-to-6:00 P.M. hour. Determine the following probabilities assuming that an auto has just arrived.

a. What is the probability that the next auto will arrive within 6 seconds (0.1 minute)?

b. What is the probability that the next auto will arrive within 3 seconds (0.05 minute)?

c. What are the answers to (a) and (b) if the rate of arrival of autos is 60 per minute?

d. What are the answers to (a) and (b) if the rate of arrival of autos is 30 per minute?

The probability that the next auto will arrive within 11 second is?

Explanation / Answer

a) P(arrival time 0.1) =1 –e^{–(50)( 0.1)} = 0.9933

b) P(arrival time 0.05) =1 –e^{–(50)( 0.05)} = 0.9179

c) P(arrival time 0.1) =1 –e^{–(60)( 0.1)} = 0.9975

P(arrival time 0.1) =1 –e^{–(60)( 0.05)} = 0.95

d) P(arrival time 0.1) =1 –e^{–(30)( 0.1)} = 0.95

P(arrival time 0.1) =1 –e^{–(30)( 0.05)} = 0.7769

e) P(arrival time 0.1) =1 –e^{–(50)( 0.183)} = 0.167

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