At Miami University, Oxford Campus, students arrive at the Bursar Services Office at an average of one every $15$ minutes, and their requests take on average $10$ minutes to be processed. The MU Bursar service counter is staffed by only one clerk, Mary Booso, who works eight hours per day. Assume Poisson arrivals and exponential service times.

a$.$ What percentage of time is Mary idle? $($Round your answer to $1$ decimal place.$)$

Percentage of time $\%$