Respuesta :
Using the Central Limit Theorem, it is found that the standard deviation for the sampling distribution of the sample proportions is of 0.062.
What does the Central Limit Theorem states?
It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
In this problem:
- The proportion is of p = 0.26.
- A sample of n = 50 families is taken.
Hence, the standard deviation is given by:
[tex]s = \sqrt{\frac{0.26(0.74)}{50}} = 0.062[/tex]
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
