Respuesta :
Answer:
By the Central Limit Theorem, it is approximately normal with mean 0.29 and standard deviation 0.0596
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
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]
According to the U.S. Census Bureau, 29% of Americans age 25 years or older have already earned a bachelor's or more advanced degree.
This means that [tex]p = 0.29[/tex]
You decide to randomly select 58 adults over the age of 25 to ask if they have earned at least a bachelor's degree.
This means that [tex]n = 58[/tex]
Describe the sampling distribution of the proportion of respondents who have earned at least a bachelor's degree.
By the Central Limit Theorem, it is approximately normal with mean [tex]\mu = p = 0.29[/tex] and the standard deviation is [tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.29*0.71}{58}} = 0.0596[/tex]
