Question

An elementary school has a population of 635 students, 600 of whom have received the chicken pox vaccine. The school nurse wants to make sure that the school meets all state requirements for vaccinations at public schools.
Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=120.

Answer 1

Answer with explanation:

Given : An elementary school has a population of 635 students, 600 of whom have received the chicken pox vaccine.

Then population proportion = $p=\dfrac{600}{635}=0.944881889764\approx0.945$

For n=120

The mean and standard deviation of the sampling distribution of the sample proportions is given by :-

$\mu_{\hat{p}}=p=0.945$

$\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}\\\\ =\sqrt{\dfrac{0.945(1-0.945)}{120}}\\\\=0.0208116553883\approx0.021$

Thus, the mean and standard deviation of the sampling distribution of the sample proportions is given by :-

$\mu_{\hat{p}}=0.945$

$\sigma_{\hat{p}}=0.021$