Need help with this. Ignore the parts about pings, I already did them. I just mostly need to know how to calculate these numerical answers.

This exercise explores of the impact of the switching time $($time spent on routers, switches or other intermediary networking devices$)$ and the propagation time $($impacted by distance$).$A factor in the delay of a store$-$and$-$forward packet$-$switching system is the switch time, $-$namely the time it takes to store and forward a packet through a switch $($router $($L$3$ switch$)$ or L$2$ switch$).$ The objective of this exercise is to investigate the impact of the switch time on the overall delivery delay of a packet. The switch time is about $5$ se per device: we assume $($oversimplification$)$ that each device adds this switching time to the packet delay in order to process $($routing$...)$ the packet. Consider a packet P sent from Auburn University $($AU$)$ to Stanford University $($about $4,000$ kms from Auburn$)$ over a copper line. Assume the propagation speed in copper to be $2/3$ the speed of light.

a$)(32$ points$)$ What is the propagation time from the packet P to reach the destination? Ping www$.$stanford.edu Insert here a screenshot of your ping collecting at least $15$ ping packets. The ping must be executed on some Unix tux machine on the Engineering network. Your screenshot should look like this template screenshot $($we should see the username, the date, the commands typed, and the results$)$: Failing to post the screenshot or not providing all the required information will result in a $50$ points penalty. Providing a screenshot of this task on your local machine will result in a $50$ points penalty.Report here the minimum, average, and maximum round trip time collected using Ping. Recall that the one way transit can be estimated as half the round trip time. Check$/$discuss whether your calculations $($to determine the one way propagation time from source to destination$)$ somewhat matches the ping measurements. If the calculations do not match the ping measurement, propose possible explanations.

b$)(16$ points$)$ Provide the approximate number of switches $($routers$)$ between a computer at Auburn University and a computer at the destination. Provide the answer and do not forget to write how you found the answer. Use the command traceroute on some Unix Tux machine. Let us know if you encounter difficulties.$).$ Note that these commands do not reveal L$2-$switches. Provide a screenshot of the traceroute. Your screenshot should look like the template screenshot above $($we should see the username, the date, the commands typed, and the results$)$: Failing to post the screenshot or not providing all the required information will result in a $50$ points penalty. Providing a screenshot of this task on your local machine will result in a $50$ points penalty.

c$)(20$ points$)$ Assuming that there are about $15$ switches between AU and the destination, what is the ratio of the total switch time to the propagation time? Is the switching time a major component in the total delivery time? Discuss.

d$)(32$ points$)$ How many switches should there be between AU and the destination such that the switch time is equal to the propagation time? Discuss the impact of propagation time and the processing$/$switching times on the intermediary nodes. Which parameter impacts more delay on networks, propagation time or switching time?