Question

Suppose a candidate for public office is favored by only 48% of the voters. if a sample survey randomly selects 2500 voters, the percentage in the sample who favor the candidate can be thought of as a measurement from a normal curve with a mean of 48% and a standard deviation of 1%. based on this information, how often would such a survey show that 50% or more of the sample favored the candidate?

Answer 1

Mean=0.48
standard deviation=0.01
thus using the z-score:
P(x>0.5) we shall have the following:
z=(0.5-0.48)/0.01=2
thus
P(x>0.5)
=1-P(x<0.5)
=1-P(z<2)
=1-0.9772
=0.0228