Value with z = 2, mean 50, sd 4

Step by step

The question

Question: which number has a z-score of 2, when the mean is 50 and the SD is 4?

A z-score of 2 means 2 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.

Careful!

Times comes before plus: first z times the SD, then add the mean.

2 Put the numbers in

2 times 4 is 8.

50 plus 8 is 58.

3 Read it

58 on the number line: 2 SDs above the mean.

4 Check

Let's check: the z-score of 58 is 58 minus 50, over 4.

That is 2.

So it is right!

Let's look back.

First: write the formula.

Then: put the numbers in.

Then: read it.

Last: check.