Question

Use normal approximation to find the probability of the indicated number of voters. In this case, assume that 153 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 36 voted. The probability that 36 of 153 eligible voters voted is?

Answer 1

did you get it started

Answer 2

$$
\Large P(x\leq a) = \frac{1}{\sigma \sqrt {2\pi }} \int_{\infty}^{a} e^{{ - \frac{ {(x - \mu })}{2 \sigma^2} }^2 } dx\\ \text{ } \\
\\ \text{make a binomial correction factor}\\
\large P(x\leq 35.5) = \frac{1}{\sqrt{np(1-p)} \sqrt {2\pi }} \int_{\infty}^{35.5} e^{ - \frac{ {(x - np )^2 } } {2~\sqrt{np(1-p)}^2} } dx


$$
Alternatively you can use normal probability calculator. fewer than 36 voted normalcdf( -1x10^99, 35.5, 153*.22 , sqrt(153*.22*.78))

Answer 3

By the Central Limit Theorem, we have: