Standard normal distribution

Definition

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is used as a reference to transform any normal distribution into a standardized form for easier analysis.

5 Must Know Facts For Your Next Test

1. The total area under the standard normal distribution curve is equal to 1.
2. The curve is symmetric about the mean, which is 0.
3. Approximately 68% of the data falls within one standard deviation from the mean (between -1 and 1).
4. Z-scores are used to represent values on the standard normal distribution, indicating how many standard deviations an element is from the mean.
5. The empirical rule applies: about 95% of data falls within two standard deviations (between -2 and 2), and about 99.7% falls within three standard deviations (between -3 and 3).

Review Questions

• What are the mean and standard deviation of a standard normal distribution?
• How do you interpret a Z-score in terms of its distance from the mean?
• What percentage of data lies within two standard deviations in a standard normal distribution?

Related terms

Z-Score:

A measure that describes how many standard deviations an element is from the mean.

Empirical Rule:

A rule stating that for a normal distribution, nearly all data will fall within three standard deviations of the mean.

Normal Distribution:

A continuous probability distribution characterized by its bell-shaped curve, symmetric around its mean.