In this article, we will discuss step by step guide on how to find the area between two z scores on both sides of the mean.

Find the area between two z scores

Step to find the area between two z scores:

  • Step 1: Find the area for the two z-scores using the z-score table.

  • Step 2: Subtract the smaller area from the greater area.

the area between the two z = larger area – smaller area (calculated)

  • Step 3: The resultant is the required area between the two z-scores.

Let’s understand to find the area between two z-scores on both sides of the mean using an example.

How to find the area between -0.48 and 1.56

To find the area between two z-scores, follow the below steps:

Step 1: Find the area left to the z = -0.48

  • Choose a negative z-table as the given z-score (i.e -0.48) is negative.

  • Check the area value for the given z in the z-table.

  • Look at the first two digits (-0.4) of the z-score on the left side column (y-axis) of the z-table and then the remaining number (0.08) on the x-axis on the top row.

Area to the left of z score

  • The intersection of the two is 0.3156 (highlighted in red).

area to the left of -0.48 is 0.3156

Step 2: Find the area left to the z = 1.56

  • Choose a positive z-table as the given z-score (i.e 1.56) is positive.

  • Check the area value for the given z in the z-table.

  • Look at the first two digits (1.5) of the z-score on the left side column (y-axis) of the z-table and then the remaining number (0.06) on the x-axis on the topmost row.

The area to the left of the z score

  • The intersection of the two is 0.9406 (highlighted in red).

area to the left of 1.56 is 0.9406

Step 3: Subtract the smaller area from the greater area

The area between the two z scores = larger area – smaller area (calculated)

The area between two z = area to the left of 1.56 – area to the left of -0.48

Area between two z scores = 0.9406 – 0.3156 = 0.6250

The area between two scores

Step 4: The resultant is the required area between the two z-scores.

Area between -0.48 and 1.56 = 0.6250

Conclusion

I hope the above article to find the area between two z scores on both sides of the mean using step by step guide is helpful to you.

In the above example, we calculate the area to the left for the given z and later find the area between the two z-scores.