Assignment 1

1. For each of the random variables defined below, indicate whether the random value is a discrete or continuous variable.

Inter-arrival time of customers Number of customers arriving at a bank Waiting time for customers waiting in a queue Number of vehicles required to serve a distribution company. Service time at a teller in a bank Distance travelled by a forklift in a warehouse. Defective rate in a production center. Number of daily defects found in the output of a production center.

2. The arrival times of the customers at two branches of a company are recorded as follow:

Customer No Arrival time branch (A) Arrival time branch (B)1 8:04:00 AM 8:04:00 AM2 8:09:00 AM 8:09:00 AM3 8:12:00 AM 8:12:00 AM4 8:15:00 AM 8:13:00 AM5 8:19:00 AM 8:15:00 AM6 8:24:00 AM 8:19:00 AM7 8:28:00 AM 8:24:00 AM8 8:32:00 AM 8:28:00 AM9 8:37:00 AM 8:32:00 AM

10 8:40:00 AM 8:37:00 AM11 8:44:00 AM 8:40:00 AM12 8:49:00 AM 8:44:00 AM13 8:53:00 AM 8:49:00 AM14 8:58:00 AM 8:53:00 AM15 9:02:00 AM 8:58:00 AM16 9:07:00 AM 9:02:00 AM17 9:10:00 AM 9:06:00 AM18 9:13:00 AM 9:09:00 AM19 9:17:00 AM 9:12:00 AM20 9:22:00 AM 9:22:00 AM

Compute the descriptive statistics that define the inter-arrival time of customers if the company starts it business at 8:00 AM.

1

What is the difference between the inter-arrival time at branch B in comparison to the inter-arrival time at branch A?

3. Given the service time of the first 10 customers arriving at branch A, compute the descriptive statistics of the time spent in the system.

Customer No

Arrival time branch (A)

Service time

1 8:04:00 AM 82 8:09:00 AM 83 8:12:00 AM 44 8:15:00 AM 65 8:19:00 AM 76 8:24:00 AM 77 8:28:00 AM 78 8:32:00 AM 49 8:37:00 AM 4

10 8:40:00 AM 5

2