MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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