Question 1181530
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.
<a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>
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.


<img src = "http://theo.x10hosting.com/2021/060701.jpg">


<img src = "http://theo.x10hosting.com/2021/060702.jpg">


<img src = "http://theo.x10hosting.com/2021/060703.jpg">