Respuesta :
Answer:
The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.
Step-by-step explanation:
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]
In this question:
[tex]p = 0.75, n = 30[/tex]
So
[tex]\mu = 0.75, s = \sqrt{\frac{0.75*0.25}{30}} = 0.0791[/tex]
The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.
