Respuesta :
Answer:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
[tex] \mu_{\bar X} = 4.09[/tex]
[tex]\sigma_{\bar X}= \frac{\sigma}{\sqrt{n}}= \frac{0.08}{\sqrt{16}}= 0.02[/tex]
So the best answer for this case would be:
[tex]\bar X \sim N (4.09, \frac{0.08}{\sqrt{16}}= 0.02)[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the costs of unleaded gasoline of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(4.09,0.08)[/tex]
Where [tex]\mu=4.09[/tex] and [tex]\sigma=0.08[/tex]
We select a sample size of n =16. Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
[tex] \mu_{\bar X} = 4.09[/tex]
[tex]\sigma_{\bar X}= \frac{\sigma}{\sqrt{n}}= \frac{0.08}{\sqrt{16}}= 0.02[/tex]
So the best answer for this case would be:
[tex]\bar X \sim N (4.09, \frac{0.08}{\sqrt{16}}= 0.02)[/tex]
