Sampling Distribution and PRobability

Question

the proportion of eligible voters in the next corporation election who will vote for the incumbent is assumed to be 55%. what is the probability that in a random sample of 500 voters less than 49% say they will vote for the incumbent? write your conclusion.

full step by step guide is needed

Answer 1

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

where phat = 0.49, p = 0.55 and n = 500

P(phat < 0.49) = P(z < (0.49-0.55)/sqrt(0.55 * 0.45/500) = P(z < -2.7) = 0.0035