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.
Z-Score Tip: How to calculate the z score using Z-score Calculator!
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.
- 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 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
Step 4: The resultant is the required area between the two z-scores.
area between -0.48 and 1.56 = 0.6250
Z-Score Tip: Do you know, how to Calculate Z Score in Excel!
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.
You can also find the area between two negative z-scores by finding the areas and subtracting the smaller area from the larger area.
You can find more topics about Z-Score and how to calculate z score given the area on the ZScoreGeek home page.