Respuesta :
Answer:
The mean of the sampling distribution of the sample proportions is 0.62 and the standard deviation is 0.0485.
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]
62% of the households have cable tv.
This means that [tex]p = 0.62[/tex]
Sample of 100.
This means that [tex]n = 100[/tex]
What is the mean and standard deviation of the sampling distribution of the sample proportions?
[tex]\mu = p = 0.62[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.62*0.38}{100}} = 0.0485[/tex]
The mean of the sampling distribution of the sample proportions is 0.62 and the standard deviation is 0.0485.
