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# How to Find Area to the Left of Z-Score (With Examples)

In statistics, a z-score tells us how many standard deviations away a given value lies from a population mean.

We use the following formula to calculate a z-score for a given value:

z = (x â€“ Î¼) / Ïƒ

where:

• x: Individual data value
• Î¼: Mean of population
• Ïƒ: Standard deviation of population

To find the area under a normal distribution that lies to the left of a given z-score, we can use one of two methods:

1. Use the z table.

2. Use the Area to the Left of Z-Score Calculator.

The following examples show how to use each of these methods in practice.

### Example 1: Area to the Left of Negative Z-Score

The weight of a certain species of turtles is normally distributed with mean Î¼ = 300 pounds and standard deviation Ïƒ = 15 pounds. Approximately what percentage of turtles weigh less than 284 pounds?

The z-score for a weight of 284 pounds would be calculated as z = (284 â€“ 300)Â  / 15 = -1.07

We can use one of two methods to find the area to the left of this z-score:

Method 1: Use z table.

To find the area to the left of the z-score, we can simply look up the value -1.07 in the z-table:

The area to the left of z = -1.07 is 0.1423.

Applied to our scenario, this means approximately 14.23% of turtles weight less than 284 pounds.

Method 2: Use Area to the Left of Z-Score Calculator

We can also use the Area to the Left of Z-Score Calculator to find that the area to the left of z = -1.07 is 0.1423.

### Example 2: Area to the Left of Positive Z-Score

The scores on a certain exam are normally distributed with mean Î¼ = 85 and standard deviation Ïƒ = 8. Approximately what percentage of students score less than 87 on the exam?

The z-score for an exam score of 87 would be calculated as z = (87 â€“ 85)Â  / 8 = 0.25

We can use one of two methods to find the area to the left of this z-score:

Method 1: Use z table.

To find the area to the left of the z-score, we can simply look up the value 0.25Â in the z-table:

The area to the left of z = 0.25 is 0.5987. Applied to our scenario, this means approximately 59.87%Â of students score less than 87 on this exam.

Method 2: Use Area to the Left of Z-Score Calculator

We can also use the Area to the Left of Z-Score Calculator to find that the area to the left of z = 0.25 is 0.5987.