Step by step
The question
Question: find the z-score of 18, when the mean is 25 and the SD is 3.
z-score of 18: mean 25, SD 3
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 18 − 253 ✗
2 Put the numbers in
The top first: 18 minus 25 is −7.
Then −7 divided by 3 is about −2.33.
z = 18 − 253 = −73 ≈ −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.
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.
So it is right!
25 + (−2.33) × 3 = 18.01
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
z = 18 − 253 = −73 ≈ −2.33