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 to standardize scores from different normal distributions for comparison.

5 Must Know Facts For Your Next Test

1. The total area under the curve of a standard normal distribution is equal to 1.
2. Approximately 68% of the data falls within one standard deviation from the mean, 95% within two, and 99.7% within three.
3. Z-scores represent the number of standard deviations a data point is from the mean in a standard normal distribution.
4. The probability density function (PDF) of the standard normal distribution is given by $f(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}$.
5. Standardizing a variable involves converting it into z-scores using the formula $z = \frac{x - \mu}{\sigma}$.

Review Questions

• What are the mean and standard deviation of a standard normal distribution?
• How do you interpret a z-score in relation to the standard normal distribution?
• What percentage of data falls within two standard deviations from the mean in a standard normal distribution?

Related terms

Normal Distribution: A type of continuous probability distribution for a real-valued random variable, characterized by its bell-shaped curve.

Z-Score:

A measure that describes how many standard deviations a data point is from the mean.

Probability Density Function (PDF):

A function that describes the likelihood of a random variable taking on a range of values.