A small diner has one employee and a counter with seating for 8 customers. The diner does not package food for takeout. Customers arrive at the diner at the rate of 20 per hour (Poisson distributed). Service times are exponentially distributed and average 24 per hour. Customers that arrive when all seats are taken do not enter the diner. What is the probability that there are no customers in the diner?
A) 0.2068
B) 0.7933
C) 0.8333
D) 0.1667

Question

Quizplus · Accepted Answer

The probability that there are no customers in the diner is equal to the probability that the number of arrivals is less than or equal to the number of departures. The arrival rate is 20 per hour and the service rate is 24 per hour, so the probability that there are no customers in the diner is equal to the probability that the number of arrivals is less than or equal to 8. This probability is given by the Poisson distribution with parameter 20/24 = 5/6, and is equal to 0.2068.

A Small Diner Has One Employee and a Counter with Seating