Cars arrive randomly and independently at a drive through service centre at a rate of 10 per hour. What is the probability that no cars will arrive in a 15 minute period?
A) 0.0821
B) 0.0067
C) 0.0250
D) 0.00
E) 0.1353

Question

Quizplus · Accepted Answer

The arrival of cars can be modeled as a Poisson process with a rate of 10 cars per hour. For a 15-minute period, the rate is 10/4 = 2.5 cars. The probability of no cars arriving (k=0) is given by the Poisson probability mass function: P(X=0) = (e^(-λ) * λ^k) / k! = (e^(-2.5) * 2.5^0) / 0! = e^(-2.5) ≈ 0.0821.

Cars Arrive Randomly and Independently at a Drive Through Service