Answer:
[tex]a.\ \mu_p=750\ \ , \sigma_p=0.005\\\\b.\ \mu_p=150\ \ , \sigma_p=0.0113\\\\c.\ \mu_p=75\ \ , \sigma_p=0.0160[/tex]
Step-by-step explanation:
a. Given p=0.15.
-The mean of a sampling proportion of n=5000 is calculated as:
[tex]\mu_p=np\\\\=0.15\times 5000\\\\=750[/tex]
-The standard deviation is calculated using the formula:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.15(1-0.15)}{5000}}\\\\=0.0050[/tex]
Hence, the sample mean is μ=750 and standard deviation is σ=0.0050
b. Given that p=0.15 and n=1000
#The mean of a sampling proportion of n=1000 is calculated as:
[tex]\mu_p=np\\\\=1000\times 0.15\\\\\\=150[/tex]
#-The standard deviation is calculated as follows:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{1000}}\\\\\\=0.0113[/tex]
Hence, the sample mean is μ=150 and standard deviation is σ=0.0113
c. For p=0.15 and n=500
#The mean is calculated as follows:
[tex]\mu_p=np\\\\\\=0.15\times 500\\\\=75[/tex]
#The standard deviation of the sample proportion is calculated as:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{500}}\\\\\\=0.0160[/tex]
Hence, the sample mean is μ=75 and standard deviation is σ=0.0160
