Finding Areas Under the Normal Curve
1) We can easily find areas like the one below.
a) First, find the distance that xi is from the mean and then divide this distance by the
size of the standard deviation. The result will be Z xi .
Z xi 
xi  

b) Look up the area in the Z-table.
2) Because the normal cure is symmetric about the mean, repeat step ‘a’ in 1) and
look up the absolute value of in the Z-table to find the area.
3) In this example you must find two Z values. Find Z xi , Z x j and then look up | Z xi |
and Z x j in the Z-table to get the areas. Add the two areas together.
4) Finding the area in the tail below requires two steps. Remember: we know that
the entire area to the right of  is equal to 0.5.
a) Find the area under the curve from  to xi in the usual way. We’ll call
this area A1.
b) Subtract A1 from 0.5. 0.5 – A1 = Area in tail
5) In the example bellow we must find two areas: the area from  to xi (Ai) and the
area from  to xj (Aj). Our area of interest will be Aj – Ai.