Problem $15-5$ The reference desk of a university library receives requests for assistance. exponential probability distribution with a service rate of $12$ requests per hour.

a$.$ What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.

$P_0=$

b$.$ What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.

$L_q=$

c$.$ What is the average waiting time in minutes before service begins? If required, round your answer to four decimal places.

$W_Q=,$ thours

d$.$ What is the average time at the reference desk in minutes $($waiting time plus service time$)?$ If required, round your answer to one decimal place.

$W=,$ hours

e$.$ What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.

$P_w=$