A single Automated Teller Machine $($ATM$)$ is located on the ground floor of a busy building. Service time at this machine is exponentially distributed. On average, the ATM machine can serve a customer in $2$ minutes $(30$ customers an hour$).$ Customer arrivals at the machine are Poisson distributed, with an average of $25$ customers an hour. Relevant formulas to analyze this $\frac{M}{M}\frac{?}{1}$ model are available at the back of the exam. Please answer the following question, based on this information.

What is the probability that the ATM machine is idle?

A$.20\%$

B$.5\%$

C$.83\mathrm{.}33\%$

D$.16\mathrm{.}67\%$

E$.0\%$