Final answer:
The correct network ID of a non-subnetted TCP/IP network using the example IP range is 192.168.1.0, which signifies all devices on that specific network.
Step-by-step explanation:
When dealing with TCP/IP networks that are not subnetted, the network ID is identified by the first three octets, ending with a zero to represent all hosts on that network. Therefore, given the options provided, the correct network ID of the network you administer would be 192.168.1.0. In TCP/IP networking, the network ID (also known as the network address) is used to refer to all devices on the same network and is determined based on the subnet mask that groups a certain range of IP addresses into one network. Since the network is not subnetted, we assume a standard class C subnet mask of 255.255.255.0, which means the first three octets define the network portion, and the last octet designates the host portion within that network.