Answer to Question #312598 in Statistics and Probability for maggie

Question

A poll is given, showing 80% are in favor of a new building project.

If 7 people are chosen at random, what is the probability that fewer than 5 of them favor the new building project? 

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

Answer 1

The number of people in favor is $X\sim Bin\left( 7,0.8 \right)$

$P\left( X<5 \right) =1-P\left( X\geqslant 5 \right) =1-P\left( X=5 \right) -P\left( X=6 \right) -P\left( X=7 \right) =\\=1-C_{7}^{5}\cdot 0.8^5\cdot 0.2^2-C_{7}^{6}\cdot 0.8^6\cdot 0.2-0.8^7=0.148032$