Question

A poll is given, showing 35% are in favor of a new building project.

If 9 people are chosen at random, what is the probability that at least 5 of them favor the new building project? 

Probability =    (Please show your answer to 4 decimal places)

Answer 1

$X\sim Bin\left( 9,0.35 \right) \\P\left( X\geqslant 5 \right) =P\left( X=5 \right) +P\left( X=6 \right) +P\left( X=7 \right) +P\left( X=8 \right) +P\left( X=9 \right) =\\=C_{9}^{5}\cdot 0.35^5\cdot \left( 1-0.35 \right) ^4+C_{9}^{6}\cdot 0.35^6\cdot \left( 1-0.35 \right) ^3+C_{9}^{7}\cdot 0.35^7\cdot \left( 1-0.35 \right) ^2+C_{9}^{8}\cdot 0.35^8\cdot \left( 1-0.35 \right) +0.35^9=0.171719$