Step by step
The question
Question: X is normal, with mean 80 and SD 6: which value has 50% below it?
A value with 50 percent below it is also called the 50th percentile.
1 Shade the area
The bell, with the mean 80 in the middle.
x is the cut-off we want.
50 percent is below x: we shade it, on the left of x.
2 Area to the left
The z-table works with the area to the left of z.
50 percent is 0.5.
It is already on the left.
Careful!
More than half the bell is on the left.
So x is above the mean, and z is positive.
3 Find it inside the table
Now we look for 0.5000 inside the table.
0.5000 is in the table: row 0.0, column .00.
So z = 0.
4 Back to x
Start at the mean, then go z SDs: x is the mean plus z times the SD.
0 times 6 is 0.
80 plus 0 is 80.
5 Check
Let's check: the z of 80 is 80 minus 80, over 6.
That is 0.
The table at 0 gives 0.5: about 0.5 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.