Customers arrive in single server queue to be serviced accor

Customers arrive in single server queue to be serviced according to Poisson process with intensity 5 customers an hour. That is, there is a single server who services each customer in the order they arrive while all the customers wait in line.

a) If the customers begin to arrive at 8am, find the probability that at least 4 customers arrived between 9am and 10am.

Solution

X: NO of customers in an hour is a poisson variable with mean = 5

the probability that at least 4 customers arrived between 9am and 10am.=P(X>=4)

= 0.7350