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In a health clinic, the average rate of arrival of patients is 12 per hour. On an average, a doctor can serve patients at the rate of one patient every four minutes. Find the utilization factor.
  • a)
    0.2
  • b)
    0.8
  • c)
    1
  • d)
    0.5
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a health clinic, the average rate of arrival of patients is 12 per...
λ = 12/hour
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In a health clinic, the average rate of arrival of patients is 12 per...
Given:
- Average rate of arrival of patients = 12 per hour
- Average rate at which a doctor can serve patients = one patient every four minutes

To Find:
Utilization factor

Solution:
Utilization factor is defined as the ratio of the service rate to the arrival rate. It represents the percentage of time that the server is busy serving the patients.

Utilization Factor = Service Rate / Arrival Rate

Step 1: Convert the arrival rate to minutes
- Arrival Rate = 12 per hour
- 1 hour = 60 minutes
- Arrival Rate = 12 per 60 minutes
- Arrival Rate = 0.2 per minute

Step 2: Convert the service rate to minutes
- Service Rate = one patient every four minutes
- Service Rate = 1 per 4 minutes
- Service Rate = 0.25 per minute

Step 3: Calculate the utilization factor
- Utilization Factor = Service Rate / Arrival Rate
- Utilization Factor = 0.25 per minute / 0.2 per minute
- Utilization Factor = 1.25

Step 4: Convert the utilization factor to a percentage
- Utilization Factor = 1.25 * 100%
- Utilization Factor = 125%

Answer:
The utilization factor is 125%, which can be approximated to 0.8 (option B).
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In a health clinic, the average rate of arrival of patients is 12 per hour. On an average, a doctor can serve patients at the rate of one patient every four minutes. Find the utilization factor.a) 0.2b) 0.8c) 1d) 0.5Correct answer is option 'B'. Can you explain this answer?
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