# 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 – μ) / σ

where:

• x: Individual data value
• μ: Mean of population
• σ: 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 μ = 300 pounds and standard deviation σ = 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 – 300)  / 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 μ = 85 and standard deviation σ = 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 – 85)  / 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 0.25 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% 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. 