solexfinal

# The correct answer is e square solution of problem

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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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