Question

uppose that the proportion of successes in a population is ? and that a very large simple random sample of size ? is obtained from that population. What does the central limit theorem say about the distribution of the sample proportion? The sample proportion has mean equal to ? and standard deviation equal to ?(1−?)?⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√. The sample proportion is approximately normally distributed if the sample is large enough. The sample proportion is binomially distributed with parameters ? and ?. The sample proportion has mean equal to the population mean ? and standard deviation equal to ??⎯⎯√.

Answer 1

Let $\hat{p}$ denotes the sample proportion.

According to central limit theorem,

$\hat{p} \overset{a}{\sim} Normal(p, \frac{p(1-p)}{n})$

ans-> The sample proportion is approximately normally distributed if the sample is large enough.