Step by step
The question
Question: find the z-score of 45, when the mean is 50 and the SD is 5.
z-score of 45: mean 50, SD 5
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 45 − 505 ✗
2 Put the numbers in
The top first: 45 minus 50 is −5.
Then −5 divided by 5 is −1.
z = 45 − 505 = −55 = −1
3 Read it
45 on a number line with the SD marks.
The z numbers count the SDs.
So 45 is 1 SD below the mean.
1 SD below the mean
4 Check
Let's check: start at the mean and go −1 SDs.
50 plus −1 times 5 is 45.
So it is right!
50 + (−1) × 5 = 45
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
z = 45 − 505 = −55 = −1