Question

A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 3.0 per minute. In serving themselves, customers take about 14 seconds, exponentially distributed. a. How many customers would you expect to see, on average, at the coffee urn? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer: 3 customers.

Step-by-step explanation:

Given the following :

Arrival rate of customers = 3 customers per minute

Service time = 14 seconds

Then if service time is 14 seconds, the service rate per minute will be 60/14 = 4.29 = 4 (nearest whole number)

Service rate = 4 customers per minute.

Number of customers at coffee urn(Nc) :

Nc = (arrival rate) /(service rate - arrival rate)

Nc = (3) / (4 - 3)

Nc = 3 / 1

Nc = 3

Therefore, average number of customers expected at coffee urn = 3