The correct answer is
(e)
.
square
Solution of problem 1.11:
Let
x
denote the number of students who tossed
hh
and cheated, and let
y
denote the number of students who tossed
hh
and did not cheat. Then we have that roughly 4
x
= 4 or
x
= 1. Since
the number of people who tossed
hh
is about 100
/
4 = 25 it follows that
y
= 25

1 = 24. In particular about 3
x
+
y
= 27 people have said
“yes”, and about
x
+ 3
y
= 73 people said “no”.
The correct answer is
(f)
.
square
16
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Solution of problem 1.12:
Out of the 720 people surveyed, 180 are college
students.
Based on this statistical sample the proportion of college
students in the town population is 180
/
720 = 1
/
4.
Thus about a
quarter of the twon population is 8
,
000 people. Then the remaining
three quarters of the town population are 3
·
8
,
000 = 24
,
000.
The correct answer is
(a)
.
square
Solution of problem 1.13:
Let
I
be the annual percentage rate on the
account. Then we have
1681 = 1600
parenleftbigg
1 +
I
100
parenrightbigg
2
,
or
I
= 100
parenleftBigg
radicalbigg
1681
1600

1
parenrightBigg
=
100
40
= 2
.
5
.
The correct answer is
(e)
.
square
Solution of problem 1.14:
The
(system rationality)
property does not
hold for this voting system: ties are possible for the total numerical
scores.
The
(determinism)
property holds: only the ranking preferences of
the voters are taken into account in determining the outcome of the
vote.
The
(consensus)
property holds: if all voters rank
A
higher than
B
,
then
A
will have a lower numerical score than
B
, and so will rank higher
than
B
in the outcome of the vote.
The
(impartiality)
property holds:
the voting system remains un
changed if we shuffle the candidates.
17
The
(independence of a third alternative)
property holds:
the
relative ranking of candidates
A
and
B
is independent of the voters
preferences for another candidate
X
since with or without
X
the nu
merical score of
A
will be lower than the numerical score of
B
.
The
(no disctators)
property holds: there are many more voters than
candidates so a low numerical score by a single voter can not pull a total
numerical score down.
The correct answer is
(a)
.
square
18
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 Spring '08
 schneps
 Natural Numbers, Rational number, Irrational number, Verhulst

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