Problem $4(15$ points$).($For part d$,$ you only need to write an expression. You don't have to carry out the numerical calculation unless you are interested.$)$

Suppose users share a $10Mbps$ link. Also suppose each user requires $200kbps$ when transmitting, but each user transmits only $10$ percent of the time. $($See the discussion of packet switching versus circuit switching in Section $1\mathrm{.}3.)$

a$.$ When circuit switching is used, how many users can be supported?

b$.$ For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting.

c$.$ Suppose there are $300$ users. Find the probability that at any given time, exactly $n$ users are transmitting simultaneously. $($Hint: Use the binomial distribution.$)$

d$.$ Find the probability that there are $51$ or more users transmitting simultaneously.