Exponentially distributed service times of a database server have an average of $0\mathrm{.}2sec.$

Queries to database server are submitted in accordance to Poisson distribution with a

mean of $120$ per minute. However, the buffer capacity is such that only $15$ queries can be

held in the buffer. Calculate:

a$)$ average response time of queries

b$)$ average waiting time of queries

c$)$ probability of $5$ or more queries in the buffer.

d$)$ probability that database server is idle