Given : An elementary school has a population of 635 students, 600 of whom have received the chicken pox vaccine.
Then population proportion = [tex]p=\dfrac{600}{635}=0.944881889764\approx0.945[/tex]
For n=120
The mean and standard deviation of the sampling distribution of the sample proportions is given by :-
[tex]\mu_{\hat{p}}=p=0.945[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}\\\\ =\sqrt{\dfrac{0.945(1-0.945)}{120}}\\\\=0.0208116553883\approx0.021[/tex]
Thus, the mean and standard deviation of the sampling distribution of the sample proportions is given by :-
[tex]\mu_{\hat{p}}=0.945[/tex]
[tex]\sigma_{\hat{p}}=0.021[/tex]
The mean and standard deviation of the sampling distribution for samples of size n=120 is: 0.945; 0.021.
Population proportion = X/N
Population proportion=600/635
Population proportion=0.945 Mean
Standard deviation=√p(1-p)/n
Standard deviation=√0.945(1-0.945)/120
Standard deviation=√0.945(0.055)/120
Standard deviation=√0.051975/120
Standard deviation=√0.000433125
Standard deviation=0.0208
Standard deviation=0.021(Approximately)
Inconclusion the mean and standard deviation of the sampling distribution for samples of size n=120 is: 0.945; 0.021.
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