Consider a sampling distribution with p equals 0.12 and samples of size n each.
Then, formula for mean = p
Formula for standard deviation= [tex]\sqrt{\dfrac{p(1-p)}{n}}[/tex]
(a) For a random sample of size n equals 5000.
Mean = 0.12
Standard deviation= [tex]\sqrt{\dfrac{0.12(1-0.12)}{5000}}[/tex]
[tex]\\\\0.00459565011723\approx0.0046[/tex]
(b) For a random sample of size n equals 1000.
Mean = 0.12
Standard deviation= [tex]\sqrt{\dfrac{0.12(1-0.12)}{1000}}[/tex]
[tex]\\\\=0.0102761860629\approx0.0103[/tex]
(c) For a random sample of size n equals 500.
Mean = 0.12
Standard deviation= [tex]\sqrt{\dfrac{0.12(1-0.12)}{500}}[/tex]
[tex]\\\\=0.0145327216997\approx0.0145[/tex]
