Round the answers to $2$ decimal places if necessary.

Question $1(3+2=5$ points$)$

The organizers of a conference in the Houston Convention Center are evaluating the possibility

of setting up a computer area where attendees can check their e$-$mail on computers provided by

the organization. There will be one common queue for all computers and only one person uses a

computer at a time. On average there are $20$ attendee arrivals per hour and the average time a

person spends on the computer is $12$ minutes

a$)$ To ensure that waiting times are not too long, the organizers want to ensure that the

utilization of the computers doesn't exceed $70$ percent. At least how many computers do

they need to have?

b$)$ The organizers of the conference have decided to buy $8$ computers. Assume that the

standard deviation of arrivals is equal to the average inter$-$arrival time, and the standard

deviation of processing times is equal to the average processing time. What is the

average waiting time $($in minutes$)$ before using the computer?