Question

The proportion of eligible voters in the next corporation election (in tumkur) 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.

Answer 1

$\hat{p}$ is normally distributed with a mean of $\mu_{\hat{p}}=p$ and a standard deviation

$$\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}$$

Given $p=0.55, n=500.$

$$P(\hat{p}<0.49)=P\bigg(Z<\dfrac{0.49-0.55}{\sqrt{\dfrac{0.55(1-0.55)}{500}} }\bigg)$$

$$\approx P(Z<-2.6968)\approx0.0035$$