The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 53,7%.

Question

What is the probability that in a random sample of 520 voters, less than 48,1% say they will vote for the incumbent?

Answer 1

z = (phat - p)/sqrt(p*(1-p)/n

where phat = sample proportion

p = population proportion

n = sample size

here phat = 0.481, p = 0.537 and n=520

z = (0.481 - 0.537)/sqrt(0.537*0.463/520) = -2.56

P(z < -2.56) = 0.0052