Step by step
The question
Question: find the z-score of 47, when the mean is 40 and the SD is 6.
z-score of 47: mean 40, SD 6
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 47 − 406 ✗
2 Put the numbers in
The top first: 47 minus 40 is 7.
Then 7 divided by 6 is about 1.17.
z = 47 − 406 = 76 ≈ 1.17
3 Read it
47 on a number line with the SD marks.
The z numbers count the SDs.
So 47 is 1.17 SDs above the mean.
1.17 SDs above the mean
4 Check
Let's check: start at the mean and go 1.17 SDs.
40 plus 1.17 times 6 is about 47.02.
So it is right!
40 + 1.17 × 6 = 47.02
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
z = 47 − 406 = 76 ≈ 1.17