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Find the area under Standard Normal Curve to the left of Z

The normal distribution is a continuous probability distribution. The total area under the standard normal curve is always 1. The normal distribution looks like a bell-shaped curve.

In this article, we will discuss step by step guide on how to find the area under the standard normal curve to the left of the z score.

Area under the Standard Normal Curve to the left of z

Steps to find the area to the left of z

Step 1: Choose between negative or positive z-table corresponding to the given z-score.

Step 2: Check the area value for the given z in the z-table.

Step 3: Look at the first two digits of the z-score on the left side column (y-axis) of the z-table and then the remaining number on the x-axis on the topmost row.

Step 4:The intersection of the two will be the required area.

Step 5: Multiply it by 100 to calculate the percentage of area.

Let’s understand find area under the standard normal curve to the left of z using an example.

Z-Score Tip: Read more on how to calculate z score!

How do you find the area to the left of z = 1.55.

To find the area to the left of given z follow the below steps:

Step 1: Choose a positive z-table as the given z-score (i.e 1.55) is positive.

Step 2: Check the area value for the given z in the z-table.

Step 3: 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 (0.05) on the x-axis on the topmost row.

Area under standard normal curve- z table
The area under the standard normal curve- z table

Step 4:The intersection of the two is 0.9394 (highlighted in red).

Step 5: Multiply it by 100 to calculate the percentage of area.

area to the left = 0.9394*100 = 93.94%

Area to the left of z
Area to the left of z

Result: The area to the left of z is 93.94% of the normal standard curve.

Z-Score Tip: Read more on how to Calculate Z Score in Excel!

Conclusion

I hope the above article to find the area under the standard normal curve to the left of z using step by step guide is helpful to you.

You can find more topics about Z-Score and how to calculate z score given the area on the ZScoreGeek home page.

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