SOLUTION: Determine the two z-scores that divide the area under the standard normal curve into a middle 0.96 area and two outside equal areas.

Question 1181530: Determine the two z-scores that divide the area under the standard normal curve into a middle 0.96 area and two outside equal areas.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the two outside areas are each equal to .02 of the normal distribution curve.
find he z-score that has an area to the left of it equal to .02.
find the z-score that has an area to the right of it equal to .02.
note that the z-score that has an area of .02 to the right of it will be equal to the z-score that has an area of .98 to the left of it (.98 = 1 minus .02).
the area between those z-scores will be equal to .96
you can do this manually through the tables, or you can use a calculator.
calculator is much easier.
i used the following calculator.
https://davidmlane.com/hyperstat/z_table.html
using this calculator, i found the z-score with .02 area to the left of it equal to -2.054 and i found the z-score with .02 area to the right of it equal to 2.054.
those same z-score gave me an area between them of .96.
here are the displays of my use of the calculator.
first is finding the z-score with area of .02 to the left of it.
second is finding the z-score with area of .02 to the right of it.
this is finding the z-scores with area of.96 between them.

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