Question one $(1)$

Icu has a local network $($LAN$)$ worth $30$ computers connected to a switch. Each Computer has a network interfere Card $($NIC$)$ with a bandwidth of $50mbps.$ The switeh has a total bandwidth of $2000Mbp.$

i$)$ If each Computer is transmitting data at an average rate of $15Mbps.$ What is the total bandWidth utilization of the LAN?

ii$)$ If the company wants to uprade the LAN to a $10-$gigabit Ethernet $(10,000Mbp)$ Connection, how many computers can be supported with the same total bandwalth utilization?

iii$)$What is the probability that exactly $8$ Computers are transmitting data simultaneously, assuming each Computer has an equal propability of transmitting or not transmitting?

iv$.)$ Find the probability that $15$ or more computers are transmitting data simultaneously.