Respuesta :
Answer:
[tex]\bar X= \mu = 25[/tex]
[tex]\sigma_{\bar X}= \frac{7}{\sqrt{15}}= 1.807[/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 variable of interest of a population, and for this case we know the following conditions
Where [tex]\mu=25[/tex] and [tex]\sigma=7[/tex]
And for this case we select a sample size of n= 15. and we want to know the distribution for the sample mean [tex]\bar X[/tex]. We can assume that the distribution for [tex]\bar X[/tex] is approximately normal and given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
Asuming that the distribution for X is also approximately normal. So then the parameters are:
[tex]\bar X= \mu = 25[/tex]
[tex]\sigma_{\bar X}= \frac{7}{\sqrt{15}}= 1.807[/tex]
