$5.[18$ points$]$ On average, $30$ people arrive at the pharmacy per hour according to a Poisson distribution, and are served in an average time of $1\mathrm{.}5$ minutes with exponential service times. Find the following:

a$)[3$ points$]$ Probability of zero customers in the system

b$)[3$ points$]$ Average utilization of the server

c$)[3$ points$]$ Average number of customers in the system

d$)[3$ points$]$ Average number of customers in line

e$)[3$ points$]$ Average time spent in the system

f$)[3$ points$]$ Average waiting time in line