Respuesta :
Answer:
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(\mu,0.08)[/tex]
Where [tex]\mu[/tex] and [tex]\sigma=0.08[/tex]
Since the distribution for X is normal then the 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]
And the standard error is given by:
[tex] SE= \frac{0.08}{\sqrt{24}}= 0.0163[/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 heights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(\mu,0.08)[/tex]
Where [tex]\mu[/tex] and [tex]\sigma=0.08[/tex]
Since the distribution for X is normal then the 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]
And the standard error is given by:
[tex] SE= \frac{0.08}{\sqrt{24}}= 0.0163[/tex]
