Question

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a? two-candidate election, if a specific candidate receives at least

55?% of the vote in the? sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 voters. Complete parts? (a) through? (c) below.

a.	What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1%

b.	What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 58%?

Answer 1

(a)

Here we have

n=100 ,p = 0.501

The sampling distribution of sample proportion will be approximately normal with mean

and standard deviation

The z-score for is

So  the probability that a candidate will be forecast as the winner is

(b)

Here we have

n=100 ,p = 0.58

The sampling distribution of sample proportion will be approximately normal with mean

and standard deviation

The z-score for is

So  the probability that a candidate will be forecast as the winner is