Honors Discrete Quiz 4.1 – 4.3 Review Guide:
Key Terms: Be able to identify and provide a definition for each of the following terms
o Seats
o Standard Quota
o Alabama Paradox
o Populations
o Upper Quotas
o New States Paradox
o States
o Lower Quotas
o Population Paradox
o Standard Divisor
o “Good” Apportionment
o Quota Rule
Be able to calculate the following:
o Standard Divisor
o Upper Quotas
o Standard Quota
o Lower Quotas
o Hamilton’s Method
Be able to interpret the meaning of the following in a given problem:
o Seats
o Populations
o States
o Standard Divisor
(1) The Google has a janitorial staff of 250 janitors working in five shifts (A, B, C, D, E).
The number of workers apportioned to each shift is based on the average number of other
Google employees working per shift, given the following table.
SHIFT
Average number of other
Google employees
a.
b.
c.
d.
e.
A
423
B
1071
C
1229
D
950
E
327
Identify the seats, states, and populations in this problem.
Calculate the standard divisor in this problem.
What does the standard divisor represent in this problem?
Find the standard quota for each shift.
Find the lower and upper quota for each shift.
(2) The Richmond has 400 new police officers. There are 6 counties and number of police
officers apportioned to each county is based on the number of crimes committed thus far
listed below:
County #1 had a 48 crimes, County #2 had a 80 crimes,
County #3 had a 62 crimes, County #4 had a 33 crimes,
County #5 had a 40 crimes, and County #6 had a 37 crimes.
a.
b.
c.
d.
e.
Identify the seats, states, and populations in this problem.
Calculate the standard divisor in this problem.
What does the standard divisor represent in this problem?
Find the standard quota for each shift.
Find the lower and upper quota for each shift.
(3) 4 students need to share a $2,000 prize they won in the lottery. They decide to apportion
money to themselves based on number of service hours accumulated.
Friend
Service Hours
a.
b.
c.
d.
e.
Joe
200
Jane
150
John
270
Jessica
180
Identify the seats, states, and populations in this problem.
Calculate the standard divisor in this problem.
What does the standard divisor represent in this problem.
Find the standard quota for each shift.
Find the lower and upper quota for each shift.
(4) The small nation is made up of four counties and has 125 seats in its Congress, which
are apportioned to the islands according to their populations under Hamilton’s Method.
County
San Andreas
San Bernadino
Santa Clara
San Diego
Population
62,400
26,160
28,480
39,120
(5) A mother has 30 pieces of candy to share among her 4 children. The mother decides to
apportion the candy based on the children’s GPA last school year. .
Child
Anthony
Bridget
Chris
Dawn
GPA
2.9
3.15
3.85
3.3
a. Show all steps to find the apportionment under Hamilton’s Method.
b. Anthony, Chris, and Dawn had done extra credit, which wasn’t originally put into
their GPAs.
Child
Anthony
Bridget
Chris
Dawn
GPA
3.0
3.15
3.9
3.5
Find the apportionment under Hamilton’s Method and state if this is an example of any
known PARADOXES.
(6) The populations of 4 states that make up a union are given in percent of actual
populations. The union has a legislature of 68 seats.
States
State #1
State #2
State #3
State #4
Population
230
600
4320
4850
a. Show all steps to find the apportionment under Hamilton’s Method.
b. A 69th seat is added to the legislature. Find the apportionment under Hamilton’s
Method and state if this is an example of any known paradoxes.