Question

Two candidates, Amy and Bob, are competing in a state election. We estimate that 55% of the voters prefer Amy. A poll is organized, and asks 100 randomly chosen voters about their preferences. Approximate the probability that at least half of that polled persons will favor Amy.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.5500
sample size       =n=	100
std error of proportion=σp=√(p*(1-p)/n)=sqrt(0.55*0.45/100) =	0.0497

from normal approximation:

probability that at least half of that polled persons will favor Amy.:

probability =P(X>0.5)=P(Z>(0.5-0.55)/0.05)=P(Z>-1.01)=1-P(Z<-1.01)=1-0.1562=0.8438