Step by step
The question
Question: X is normal, with mean 20 and SD 2: which value has 20% above it?
1 Shade the area
The bell, with the mean 20 in the middle.
x is the cut-off we want.
20 percent is above x: we shade it, on the right of x.
2 Area to the left
The z-table works with the area to the left of z.
20 percent is 0.2.
It is on the right.
So the area to the left is 1 minus 0.2: 0.8.
Careful!
0.2 is on the right.
The table needs the area to the left, 0.8.
3 Find it inside the table
Now we look for 0.8000 inside the table.
The closest number is 0.7995: row 0.8, column .04.
So z is about 0.84.
4 Back to x
Start at the mean, then go z SDs: x is the mean plus z times the SD.
0.84 times 2 is 1.68.
20 plus 1.68 is 21.68.
5 Check
Let's check: the z of 21.68 is 21.68 minus 20, over 2.
That is 0.84.
The table at 0.84 gives 0.7995: about 0.8 to the left.
So it is right!
Let's look back.
First: shade the area.
Then: area to the left.
Then: find it inside the table.
Then: back to x.
Last: check.