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Finding the Z-score from an Area in the Middle

 

Example: Find the Z-score that divides the middle 90% of the area in the standard normal distribution from the area in the tails.

 

This is an inverse normal problem and the command invNorm( area, ) is used.  In this problem the middle area is .90.  That leaves an area of .10 to be equally divided between the left and right tail areas.  Each of these areas are, therefore, equal to .05.  The Z-score that marks the lower edge of the middle area is the Z-score that corresponds to a left area of .05.

 

To find the Z-score corresponding to a left area of 0.05, press 2nd [DISTR] and select 3:invNorm( and type in .05 , 0 , 1 ) and press ENTER.

 

 

The Z-score that marks the lower edge of the middle area of .90 is -1.645.  The Z-score that marks the upper edge is 1.645 (because the normal curve is symmetry about the mean.)