Normal Distributions (Empirical Rule)

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.

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

68% of the data.

95% of the data.

0.3% of the data.

9 to 21.

Mean ± 1(Standard Deviation). For a mean of 15 and standard deviation of 3, the interval is 12 to 18.

The mean is the central value around which the data is distributed, and it is also the peak of the normal distribution curve.

It is considered an outlier, as it falls outside the range where 99.7% of the data lies.

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