Step by step
The question
Question: which number has a z-score of 0.5, when the mean is 200 and the SD is 30?
z = 0.5: mean 200, SD 30. x?
A z-score of 0.5 means 0.5 SDs above the mean.
z = 0.5: 0.5 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
0.5 times 30 is 15.
200 plus 15 is 215.
x = 200 + 0.5 × 30 = 200 + 15 = 215
3 Read it
215 on the number line: 0.5 SDs above the mean.
4 Check
Let's check: the z-score of 215 is 215 minus 200, over 30.
That is 0.5.
So it is right!
z = 215 − 20030 = 1530 = 0.5
Let's look back.
First: write the formula.
Then: put the numbers in.
Then: read it.
Last: check.
Answer
x = 200 + 0.5 × 30 = 200 + 15 = 215