Step by step
The question
Question: which number has a z-score of 2.5, when the mean is 150 and the SD is 12?
z = 2.5: mean 150, SD 12. x?
A z-score of 2.5 means 2.5 SDs above the mean.
z = 2.5: 2.5 SDs above the mean
1 Write the formula
Start at the mean, then go z SDs: x is the mean plus z times the SD.
x = mean + z × SD
Careful!
Times comes before plus: first z times the SD, then add the mean.
Careful: times first, then add
2 Put the numbers in
2.5 times 12 is 30.
150 plus 30 is 180.
x = 150 + 2.5 × 12 = 150 + 30 = 180
3 Read it
180 on the number line: 2.5 SDs above the mean.
4 Check
Let's check: the z-score of 180 is 180 minus 150, over 12.
That is 2.5.
So it is right!
z = 180 − 15012 = 3012 = 2.5
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
x = 150 + 2.5 × 12 = 150 + 30 = 180