Customers in a Small Retail Store Arrive at the Single

question 38

Essay

Customers in a small retail store arrive at the single cashier at the rate of 10 per hour. The average service time for the cashier is five minutes. Arrivals tend to follow a Poisson distribution, and service times follow an exponential distribution.
a. What is the average utilization of the cashier?
b. What is the average number of customers in the system?
c. What is the average number of customers in line?
d. What is the average time spent in the system?
e. What is the average time spent in line?

---

Definitions:

Stirrup

A small, U-shaped bone in the middle ear that plays a key role in transmitting sounds from the outer ear to the inner ear.

Cochlea

A spiral-shaped, fluid-filled inner ear structure that is essential for hearing as it converts sound vibrations into neural signals.

Auditory Nerve

The nerve that carries signals from the inner ear to the brain, allowing us to process sounds.

Eardrum

A thin membrane that separates the outer ear from the middle ear and vibrates in response to sound waves, aiding in the process of hearing.