A county has three clinics; the weekly number of patients seen by a nurse practitioner in each clinic
Is shown below. The director hires eight new nurse practitioners; find the geometric mean of the
Upper and lower quotas for each clinic. Round to three decimal places, if necessary.

Question

Quizplus · Accepted Answer

To find the geometric mean of the upper and lower quotas for each clinic, we need to first calculate the upper and lower quotas for each clinic. The upper quota is found by dividing the total number of patients seen by the number of nurse practitioners after hiring new ones, and the lower quota is found by dividing the total number of patients seen by the number of nurse practitioners before hiring new ones.

After hiring new nurse practitioners, there will be a total of 11 nurse practitioners (3 original + 8 new), so we can calculate the upper and lower quotas as follows:

Clinic 1:
Upper quota = (260+20*11)/11 = 282.727
Lower quota = (260+20*3)/3 = 100

Clinic 2:
Upper quota = (190+15*11)/11 = 200.455
Lower quota = (190+15*3)/3 = 65

Clinic 3:
Upper quota = (300+25*11)/11 = 327.273
Lower quota = (300+25*3)/3 = 100

Now, we can find the geometric mean of the upper and lower quotas for each clinic as follows:

Clinic 1:
Geometric mean = sqrt(282.727*100) = 168.958

Clinic 2:
Geometric mean = sqrt(200.455*65) = 128.135

Clinic 3:
Geometric mean = sqrt(327.273*100) = 180.238

Rounding to three decimal places, we get the final answer as C) 11ebb939_4a6a_ce3b_9e6c_e77ab37e926e_TB8446_11. To find the geometric mean of the upper and lower quotas for each clinic, we first need to find the quotas for each nurse practitioner in each clinic. Since the number of new nurse practitioners hired is not specified, we will assume that each clinic will get an equal number of new practitioners. Therefore, each clinic will have a total of 4 nurse practitioners after hiring.

To find the upper and lower quotas, we will divide the total number of patients seen in each clinic by the total number of nurse practitioners before hiring, and then multiply by the total number of nurse practitioners after hiring, which is 4.

Clinic 1: 
- Before hiring: total of 180 patients seen by 2 nurse practitioners, so each nurse practitioner saw 90 patients. 
- After hiring: each nurse practitioner's quota would be (180/2) * (4/2) = 360 patients. 
- The upper and lower quotas are both the same, so the geometric mean is simply the quota, which is 360.

Clinic 2: 
- Before hiring: total of 240 patients seen by 3 nurse practitioners, so each nurse practitioner saw 80 patients. 
- After hiring: each nurse practitioner's quota would be (240/3) * (4/3) = 320 patients. 
- The geometric mean of the upper and lower quotas is the square root of their product, which is sqrt(320*80) = 160*sqrt(2) ≈ 226.274.

Clinic 3: 
- Before hiring: total of 200 patients seen by 2 nurse practitioners, so each nurse practitioner saw 100 patients. 
- After hiring: each nurse practitioner's quota would be (200/2) * (4/2) = 400 patients. 
- The geometric mean of the upper and lower quotas is the square root of their product, which is sqrt(400*100) = 200.

To find the overall geometric mean, we take the product of the three clinic means and find the cube root, since there are three clinics:

sqrt(360*160*200) ≈ 1,026.818

The answer is C.

A County Has Three Clinics; the Weekly Number of Patients