6.4 Flashcard Normal Distributions

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

It means that the left and right sides of the distribution are mirror images of each other, indicating that the mean, median, and mode are all equal.

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations.

A standard deviation is a measure of the amount of variation or dispersion in a set of values.

The area under the normal curve represents the total probability of all outcomes, which equals 1 (or 100%).

The mean is the central point of the distribution, where the highest frequency of data points occurs.

It means that the data point is greater than the mean plus one or more times the standard deviation, indicating it is in the higher range of the distribution.