Step by step
The question
Question: find the z-score of 18, when the mean is 25 and the SD is 3.
A z-score tells how many SDs a number is from the mean.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Write the formula
x minus the mean is how far x is from the mean.
Dividing by the SD counts how many SDs that is.
So z is x minus the mean, all over the SD.
Careful!
Subtract first, then divide.
The whole top is divided by the SD.
2 Put the numbers in
The top first: 18 minus 25 is −7.
Then −7 divided by 3 is about −2.33.
3 Read it
18 on a number line with the SD marks.
The z numbers count the SDs.
So 18 is 2.33 SDs below the mean.
4 Check
Let's check: start at the mean and go −2.33 SDs.
25 plus −2.33 times 3 is about 18.01.
Not exactly 18, because −2.33 was rounded.
So it is right!
5 Pick the choice
Our answer is z ≈ −2.33.
That is choice C.
6 Why not the others
A is 2.33.
Wrong: 18 is below the mean: the sign is minus.
B is −7.
Wrong: that is the distance: divide it by the SD.
D is 6.
Wrong: divided 18 by 3.
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Then: check.
Then: pick the choice.
Last: why not the others.