Area to the left

Definition

The 'area to the left' of a given point on a normal distribution curve represents the cumulative probability that a randomly selected value from the distribution is less than or equal to that point. It is often used in conjunction with z-scores and standard normal tables.

5 Must Know Facts For Your Next Test

1. The area to the left of the mean (in a standard normal distribution) is always 0.5.
2. To find the area to the left of a z-score, you can use standard normal tables or statistical software.
3. The total area under a normal distribution curve is always 1.
4. If you need the area to the right of a z-score, subtract the area to the left from 1.
5. In real-world applications, this concept helps determine percentiles and probabilities for normally distributed data.

Review Questions

• What does an area to the left of a z-score represent in a normal distribution?
• How do you find the area to the left of a specific z-score using statistical tools?
• Why is it significant that the total area under a normal distribution curve equals 1?

Related terms

Z-Score: A measure that describes how many standard deviations an element is from the mean.

Standard Normal Distribution: A normal distribution with a mean of 0 and a standard deviation of 1.

Cumulative Probability: The probability that a random variable takes on a value less than or equal to a specific value.