Step by step
The question
Question: X is normal, with mean 250 and SD 20: which value has 1% above it?
1 Shade the area
The bell, with the mean 250 in the middle.
x is the cut-off we want.
1 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.
1 percent is 0.01.
It is on the right.
So the area to the left is 1 minus 0.01: 0.99.
Careful!
0.01 is on the right.
The table needs the area to the left, 0.99.
3 Find it inside the table
Now we look for 0.9900 inside the table.
The closest number is 0.9901: row 2.3, column .03.
So z is about 2.33.
4 Back to x
Start at the mean, then go z SDs: x is the mean plus z times the SD.
2.33 times 20 is 46.6.
250 plus 46.6 is 296.6.
5 Check
Let's check: the z of 296.6 is 296.6 minus 250, over 20.
That is 2.33.
The table at 2.33 gives 0.9901: about 0.99 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.