In a given country A and B are candidates in the current elections. It is known that 60% vote for A and 40% vote for B. A poller polls 10,000 voters in the country. Use the central limit theorem to estimate the probability of less than 6100 of the people questioned for the poll would vote for candiate A.
I have several issues:
- "60% vote A, 40% vote B" - Does that mean that if $X_i$ is a Bernoulli RV representing a vote by one of the people questioned, $X_i$ ~ $Ber(\frac{3}{5})$? Why?
- We defined the central limit theorem as follows: If $X_i$ are RVs with expectation $\mu$ and variance $\sigma^2$, then $\lim\limits_{n \to \infty} \frac{x_1+\dots+x_n - n\mu}{\sqrt{n}\sigma} = Z$ where $Z$ ~ $N(0,1)$. I think I'm then supposed to use the CDF of $Z$ to estimate $X$ - but I'm not really estimating $X$ but $Z$, no?
I know this is might be pretty simple but I'm new to this subject, hopefully this isn't a bad question.
Thank you!