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.

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:

Where the mean and  the deviation

We know that the z score is given by:

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:

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:

Where the mean and  the deviation

We know that the z score is given by:

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:

So then the correct answer for this case would be z =0.00

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step-by-step explanation: