Normally distributed

Definition

A normally distributed variable follows a symmetric, bell-shaped curve where most values cluster around the mean. It is characterized by its mean and standard deviation.

5 Must Know Facts For Your Next Test

1. The total area under the normal distribution curve is equal to 1.
2. Approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.
3. The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.
4. In hypothesis testing, if a population is normally distributed, z-scores can be used to determine probabilities.
5. A normal distribution is denoted as $N(\mu, \sigma^2)$ where $\mu$ is the mean and $\sigma^2$ is the variance.

Review Questions

• What percentage of data falls within two standard deviations of the mean in a normal distribution?
• How does the Central Limit Theorem relate to normally distributed variables?
• Why is it important to know if a dataset follows a normal distribution when conducting hypothesis tests?

Related terms

Central Limit Theorem:

States that the sampling distribution of the sample mean approaches a normal distribution as sample size increases.

Z-Score:

Measures how many standard deviations an element is from the mean.

Standard Deviation:

A measure of how spread out numbers are in a dataset.