Respuesta :
Using the Central Limit Theorem, it is found that the standard deviation of the sampling distribution of p is 0.0144.
Central Limit Theorem
- By the Central Limit Theorem, the sampling distribution of sample proportions of a proportion p in a sample of size n has mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex].
In this problem:
- Suppose that 70% of all US adults drink the cereal milk, hence [tex]p = 0.7[/tex].
- A sample of 1012 adults is taken, hence [tex]n = 1012[/tex].
Then, the standard deviation is:
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{1012}} = 0.0144[/tex]
The standard deviation of the sampling distribution of p is 0.0144.
To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/16695444
