Answer:
The population proportion is 0.1057.
For samples of size n: Mean = 0.1057, Standard deviation [tex]s = \frac{0.3075}{\sqrt{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem for Proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Population proportion:
Of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one.
This means that [tex]p = \frac{3170}{30000} = 0.1057[/tex]
The population proportion is 0.1057.
Mean and standard deviation of the sampling distribution for samples of size n
By the Central Limit Theorem, the mean is [tex]\mu = p = 0.1057[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{0.1057*0.8943}{n}} = \frac{0.3075}{\sqrt{n}}[/tex]
