Dial a Physician $($Q$12$ Q$14)$

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 always 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$6.$ On average, how many calls does the company receive in a $1-$hour period?.