Let's tackle this problem step-by-step.

Part (a): Compute the Standard Divisor

The standard divisor is calculated by dividing the total number of patients by the number of doctors available.

Given:

• Total number of patients: $7420$
• Total number of doctors: $175$

$\text{Standard Divisor} = \frac{\text{Total Patients}}{\text{Total Doctors}} = \frac{7420}{175}$

Calculating this:

$\text{Standard Divisor} = 42.4$

So, the standard divisor is 42.4.

Part (b): Compute the Standard Quota for Each Clinic

The standard quota for each clinic is calculated by dividing the average number of patients for that clinic by the standard divisor.

1. Hope Clinic: $\frac{1256}{42.4} \approx 29.62$
2. Central Clinic: $\frac{898}{42.4} \approx 21.18$
3. Nurture Clinic: $\frac{1933}{42.4} \approx 45.58$
4. Wellsway Clinic: $\frac{1202}{42.4} \approx 28.35$
5. Agape Clinic: $\frac{2131}{42.4} \approx 50.26$

Summary of Answers

• Standard Divisor: 42.4
• Standard Quotas:
  • Hope: 29.62
  • Central: 21.18
  • Nurture: 45.58
  • Wellsway: 28.35
  • Agape: 50.26

Let me know if you would like further explanation on any part of this problem or have additional questions.

Here are five related questions that expand on the concepts in this problem:

1. What would happen to the standard divisor if the number of doctors increased?
2. How does changing the total number of patients affect the standard quota?
3. What would be the impact on the quotas if an additional clinic was added with 500 patients?
4. How is the standard divisor concept useful in resource allocation in other fields?
5. Why do we round the standard quota to the nearest hundredth, and what impact might rounding have?

Tip: When calculating quotas, it’s essential to understand how small changes in numbers can affect resource distribution, which is critical in fields like healthcare.