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?

Question

Mathematics

Ivy Rhodes

15 September, 02:22

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?

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Braydon Rodgers · 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