Please help!! Statistics problem!
The UN is going to build a small clinic in a remote village in Africa to deal with the recent outbreak of a disease. The probability of having the disease is 0.35. The doctors can perform medical exams on 5 people every day. Those who are affected need to be hospitalized and treated for one day. The doctors need to decide whether to build a two-bed clinic or a three-bed clinic. The cost of a two-bed clinic is $400 per day, whereas the cost of a three-bed clinic is $570 per day. If they build a two-bed clinic, they can treat up to two patients (who are affected by the disease) in the clinic, and send the remaining possible patients (note that they can have up to 5 patients everyday) to the nearest hospital. If they build a three-bed clinic, they can treat up to three people in the clinic and send the rest of possible patients to the hospital. The cost of sending patients to the hospital (i.e., ambulance, fuel, paramedics, driver...) is $600 per patient. We are assuming that the patients who are treated in the clinic will be released by the next day so the beds will be free at the beginning of each day, and the quality and risk of treatment is the same as that of the hospital. Assume that the number of affected people out 5 people examined has a Binomial(5, 0.35) distribution and use the expected loss principle to decide which option is better: two-bed clinic or three-bed clinic.