1. Customers arrive to the checkout area of New Navy such that the interarrival rate is exponential
with rate equal to 100 customers per hour. At the checkout area, the service time of each customer is
exponentially distributed, and on average each cashier can serve 10 customers per hour. The store
has hired 12 cashiers to checkout customers and the checkout area consists of a single pool of
cashiers with one common line in front of them.
a. What is the probability that a customer’s service time is less than 19 minutes?
The customer’s service rate is exponentially distributed with average service rate of 10 customers per hour
which equals to 1/6 customer per minute. The probability that a customer’s service time is less than 19
minutes can be found using the equation below:
Pr(Service time < 19 mins) = 1 – Pr(Service time > 19 mins)
Hence,
Pr(Service time < 19 mins) = 1 – Pr(Service time > 19 mins)
Pr(Service time < 19 mins) = 0.958
