Students arrive at the Administrative Services Office at an average of one every $20$ minutes, and their requests take, on average, $15$ minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.

What percentage of time is Judy idle?

Note: Round your answer to $1$ decimal place.

How much time, on average, does a student spend waiting in line?

Note: Do not round intermediate calculations. Round your answer to $1$ decimal place.

How long is the $($waiting$)$ line on average?

Note: Round your answer to $2$ decimal places.

What is the probability that an arriving student $($just before entering the Administrative Services Office$)$ will find at least one other student waiting in line?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.