Respuesta :
Given:
p = 0.15
The mean and standard deviation(S.D) can be calculated using the formula:
[tex]\begin{gathered} \operatorname{mean}\text{ = p} \\ S\mathrm{}D\text{ = }\sqrt[]{\frac{p(1-p)}{n}} \end{gathered}[/tex](a) A random sample of size n = 4000
mean = 0.14
SD:
[tex]\begin{gathered} =\text{ }\sqrt[]{\frac{0.14(1-0.14)}{4000}} \\ =\text{ }\sqrt[]{\frac{0.1204}{4000}} \\ \approx\text{ 0.005486} \end{gathered}[/tex]SD = 0.005486
(b) A random sample of size n = 1000
mean = 0.14
SD:
[tex]\begin{gathered} =\text{ }\sqrt[]{\frac{0.14(1-0.14)}{1000}} \\ =\text{ }\sqrt[]{\frac{0.1204}{1000}} \\ \approx\text{ }0.01097 \end{gathered}[/tex]SD = 0.01097
(C) A random sample of size n = 250
mean = 0.14
SD:
[tex]\begin{gathered} =\text{ }\sqrt[]{\frac{0.14(1-0.14)}{250}} \\ =\sqrt[]{\frac{0.1204}{250}} \\ \approx\text{ 0.02195} \end{gathered}[/tex]SD = 0.02195
