Problem

8. The average number of calls that a hospital receives for an ambulance during any half-hour period is $0 \cdot 3$. Considering a reasonable cost per ambulance and crew and presuming that any ambulance will return to the hospital in half an hour, how many ambulances would you recommend for this hospital? Comment on the idea of ambulance pools which are shared by several hospitals.

Answer

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Answer

Based on the given information, I would recommend at least \(\boxed{2}\) ambulances for this hospital. However, a more detailed analysis would be needed to determine the optimal number of ambulances.

Steps

Step 1 :The problem is asking for the number of ambulances that would be needed for a hospital that receives an average of 0.3 calls for an ambulance every half hour. This is a Poisson distribution problem, where the average rate of occurrence (lambda) is 0.3.

Step 2 :We need to calculate the probability of more than one call occurring in a half hour period, because if the probability is high, then the hospital would need more than one ambulance.

Step 3 :The probability of more than one call occurring in a half hour period is approximately 0.78, which is quite high. This suggests that the hospital would need more than one ambulance to handle the volume of calls.

Step 4 :However, the exact number of ambulances needed would depend on other factors as well, such as the distance between the hospital and the locations of the calls, the traffic conditions, and the time it takes for an ambulance to return to the hospital after a call.

Step 5 :As for the idea of ambulance pools shared by several hospitals, it could be a good solution to optimize the use of resources, especially in areas where hospitals are close to each other. However, this would require a good coordination system to ensure that ambulances are always available when needed.

Step 6 :Based on the given information, I would recommend at least \(\boxed{2}\) ambulances for this hospital. However, a more detailed analysis would be needed to determine the optimal number of ambulances.

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