A company has started a phone service that uses overseas doctors to provide emergency medical consultations.
The responding doctors are based in a country with low wages but with a highly skilled pool of physicians. Responding to each call takes on average 15 minutes. At any given moment in time, there are 4 doctors overseas on duty. Calls arrive every 5 minutes on average and standard deviation of the inter-arrival time is 5 minutes. The company receives $50 from the patient's insurance company for each consultation.
If one of the 4 overseas doctors is available, the firm pays $20 to the doctor and makes $30 in profit. If no doctor is available overseas, the call is rerouted to the U.S. where a local physician answers the question.
A local physician is alw ays available to take a call. In this case, the firm pays the $50 to the local physician, so there's no profit for the company.
Q: What is the percentage of calls being answered by a physician in the US? (Write the percentage, that is, if your answer is 53.22%, input 53.22 as the answer.)