GATE 2018 ME (ME2) – Question 34
Customers arrive at a bank as a Poisson process averaging 30/hour. Find the probability that the time between successive arrivals is between 1 and 3 minutes, to two decimal places.
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Correct answer: 0.36 to 0.40
Explanation
Poisson arrivals imply exponential interarrival times. Rate is $\lambda=30/60=0.5$ per minute. Thus $$P(1<T<3)=e^{-0.5}-e^{-1.5}=0.383400.$$ Rounded answer **0.38**.