Respuesta :
Answer:
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(\mu,\sigma)[/tex]
Where [tex]\mu[/tex] the mean and [tex]\sigma[/tex] the deviation
We know that the z score is given by:
[tex] z = \frac{X -\mu}{\sigma}[/tex]
And by properties the value that separate the half area on one side and half is on the other is z=0, since we have this:
[tex] P(Z<0) =0.5[/tex]
[tex] P(Z>0)=0.5[/tex]
So then the correct answer for this case would be z =0.00
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 distribution for X is given by:
[tex]X \sim N(\mu,\sigma)[/tex]
Where [tex]\mu[/tex] the mean and [tex]\sigma[/tex] the deviation
We know that the z score is given by:
[tex] z = \frac{X -\mu}{\sigma}[/tex]
And by properties the value that separate the half area on one side and half is on the other is z=0, since we have this:
[tex] P(Z<0) =0.5[/tex]
[tex] P(Z>0)=0.5[/tex]
So then the correct answer for this case would be z =0.00
