Step by step
The question
Question: find the z-score of 72, when the mean is 65 and the SD is 4.
z-score of 72: mean 65, 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 72 − 654 ✗
2 Put the numbers in
The top first: 72 minus 65 is 7.
Then 7 divided by 4 is 1.75.
z = 72 − 654 = 74 = 1.75
3 Read it
72 on a number line with the SD marks.
The z numbers count the SDs.
So 72 is 1.75 SDs above the mean.
1.75 SDs above the mean
4 Check
Let's check: start at the mean and go 1.75 SDs.
65 plus 1.75 times 4 is 72.
So it is right!
65 + 1.75 × 4 = 72
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
z = 72 − 654 = 74 = 1.75