What value of z divides the standard normal distribution so that half the area is on one side and half is on the other? round your answer to two decimal places?

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 deviationWe 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 deviationWe 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