Step by step
The question
Question: find the z-score of 140, when the mean is 100 and the SD is 16.
z-score of 140: mean 100, SD 16
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 140 − 10016 ✗
2 Put the numbers in
The top first: 140 minus 100 is 40.
Then 40 divided by 16 is 2.5.
z = 140 − 10016 = 4016 = 2.5
3 Read it
140 on a number line with the SD marks.
The z numbers count the SDs.
So 140 is 2.5 SDs above the mean.
2.5 SDs above the mean
4 Check
Let's check: start at the mean and go 2.5 SDs.
100 plus 2.5 times 16 is 140.
So it is right!
100 + 2.5 × 16 = 140
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
z = 140 − 10016 = 4016 = 2.5