Step by step
The question
Question: find the z-score of 34, when the mean is 40 and the SD is 4.
z-score of 34: mean 40, SD 4
A z-score tells how many SDs a number is from the mean.
z = how many SDs from the mean
1 Write the formula
z is x minus the mean, all over the SD.
z = x − meanSD
Careful!
Subtract first, then divide.
The whole top is divided by the SD.
Careful: not 34 − 404 ✗
2 Put the numbers in
The top first: 34 minus 40 is −6.
Then −6 divided by 4 is −1.5.
z = 34 − 404 = −64 = −1.5
3 Read it
34 on a number line with the SD marks.
The z numbers count the SDs.
So 34 is 1.5 SDs below the mean.
1.5 SDs below the mean
4 Check
Let's check: start at the mean and go −1.5 SDs.
40 plus −1.5 times 4 is 34.
So it is right!
40 + (−1.5) × 4 = 34
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
z = 34 − 404 = −64 = −1.5