Calculate z-score of 115, mean 100, sd 15

Step by step

The question

Question: find the z-score of 115, when the mean is 100 and the SD is 15.

A z-score tells how many SDs a number is from the mean.

1 Write the formula

z is x minus the mean, all over the SD.

Careful!

Subtract first, then divide.

The whole top is divided by the SD.

2 Put the numbers in

The top first: 115 minus 100 is 15.

Then 15 divided by 15 is 1.

3 Read it

115 on a number line with the SD marks.

The z numbers count the SDs.

So 115 is 1 SD above the mean.

4 Check

Let's check: start at the mean and go 1 SDs.

100 plus 1 times 15 is 115.

So it is right!

Let's look back.

First: write the formula.

Then: put the numbers in.

Then: read it.

Last: check.