A big enterprise joint an inform about differents polls about us candidates to president. this polls give us the next dates:

people surveyed | poll confidence level | voting intention | |

candidate red | 1000 | 80% | 28% |

candidate blue | 2000 | 50% | 26% |

candidate green | 1500 | 90% | 24% |

candidate yellow | 200 | 99% | 20% |

Suppose you can show this polls to someone but not telling the numbers of survey people nor the confidence level. Select two bets you feel be able to make knowing its something really possible (and even considerably high probably)

resolve

we use the next equation in every candidate

1- candidate yellow

P +- Z*(PQ/n)^0,5*[(N-n)/(N-1)]^0,5=

0,2 +-2,58*(0,2*0,8/200)^0,5*[(1000000-200)/(999999)]^0,5=

0,2+- 2,58*0,0283*0,9999=

0,2 +- 0,073

the yellow candidate should have a voting in favor in the range between 12,7% and 27,3% percent. Considering there is a big range you should expect almost every posibility about this candidate sonsidering the poll doesn’t give us a big help.

2- candidate green

P +- Z*(PQ/n)^0,5*[(N-n)/(N-1)]^0,5=

0,24 +-1,65*(0,24*0,76/1500)^0,5*[(1000000-1500)/(999999)]^0,5=

0,24+- 1,65*0,011*0,9993=

0,24 +- 0,0181=

Then the green candidate should have a voting intention in favor between 22,19% and 25,81%. Most of surveys respect to the other candidate make a big difference respect to rightness.

3- candidate blue

P +- Z*(PQ/n)^0,5*[(N-n)/(N-1)]^0,5=

0,26 +-0,67*(0,26*0,74/2000)^0,5*[(1000000-2000)/(999999)]^0,5=

0,26+- 0,67*0,0098*0,999=

0,26 +- 0,0066=

blue candidate voting intention should be between 25,34% and 26,66%

3- candidate red

P +- Z*(PQ/n)^0,5*[(N-n)/(N-1)]^0,5=

0,28 +1,28*(0,28*0,72/1000)^0,5*[(1000000-1000)/(999999)]^0,5=

0,28+- 0,67*0,0142*0,9995=

0,28 +- 0,0095=

red candidate voting intention should be between 27,05% and 28,95%

**Possible results**

– red candidate should never be down of blue candidate, even they both are in the top compiting for first place.

– yellow candidate even considering he is on the last place can really beat red candidate.

– votes for green and yellow candidate can superb the plus of red and blue candidaten, surprisily considering they are in the top of table.