a college offers tutoring in math, english, chemistry, and biology. the number of students enrolled in each…
a college offers tutoring in math, english, chemistry, and biology. the number of students enrolled in each subject is listed below. the college can only afford to hire 13 tutors. using huntington - hills method determine the initial geometric means and the initial allocations with the standard divisor. you do not need to finish the apportionment.\n| subject | students enrolled | initial geometric mean | initial allocation |\n| ---- | ---- | ---- | ---- |\n| math | 360 | | |\n| english | 295 | | |\n| chemistry | 140 | | |\n| biology | 65 | | |\ngive decimal answers accurate to at least 3 decimal places
Answer
Explanation:
Step1: Calculate total students
Total students = $360 + 295+140 + 65=860$
Step2: Calculate standard divisor
Number of tutors = 13. Standard divisor $SD=\frac{860}{13}\approx66.154$
Step3: Calculate initial geometric mean and initial allocation for Math
Geometric mean for Math: $\sqrt{360\times(360 + 1)}=\sqrt{360\times361}\approx360.5$ Initial allocation for Math: $\frac{360}{66.154}\approx5.442$
Step4: Calculate initial geometric mean and initial allocation for English
Geometric mean for English: $\sqrt{295\times(295 + 1)}=\sqrt{295\times296}\approx295.5$ Initial allocation for English: $\frac{295}{66.154}\approx4.459$
Step5: Calculate initial geometric mean and initial allocation for Chemistry
Geometric mean for Chemistry: $\sqrt{140\times(140 + 1)}=\sqrt{140\times141}\approx140.5$ Initial allocation for Chemistry: $\frac{140}{66.154}\approx2.116$
Step6: Calculate initial geometric mean and initial allocation for Biology
Geometric mean for Biology: $\sqrt{65\times(65 + 1)}=\sqrt{65\times66}\approx65.5$ Initial allocation for Biology: $\frac{65}{66.154}\approx0.983$
Answer:
| Subject | Initial Geometric Mean | Initial Allocation |
|---|---|---|
| Math | 360.5 | 5.442 |
| English | 295.5 | 4.459 |
| Chemistry | 140.5 | 2.116 |
| Biology | 65.5 | 0.983 |