Step by step
The question
Question: find the z-score of 70, when the mean is 60 and the SD is 5.
z-score of 70: mean 60, 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 70 − 605 ✗
2 Put the numbers in
The top first: 70 minus 60 is 10.
Then 10 divided by 5 is 2.
z = 70 − 605 = 105 = 2
3 Read it
70 on a number line with the SD marks.
The z numbers count the SDs.
So 70 is 2 SDs above the mean.
2 SDs above the mean
4 Check
Let's check: start at the mean and go 2 SDs.
60 plus 2 times 5 is 70.
So it is right!
60 + 2 × 5 = 70
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
z = 70 − 605 = 105 = 2