Chapter 5 Normal Distribution Probabilities 2023

A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal. It is defined by its mean (μ) and standard deviation (σ).

The mean (μ) represents the average value of the data set and is the center of the normal distribution curve.

The standard deviation (σ) measures the dispersion or spread of the data points around the mean. A smaller standard deviation indicates that the data points are closer to the mean.

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

The z-table provides the area (probability) to the left of a given z-score in a standard normal distribution, allowing for the calculation of probabilities.

To find the probability of a z-score being less than a certain value, refer to the z-table to find the corresponding area under the curve.

The 75th percentile is the value below which 75% of the data falls. It can be found using the z-score corresponding to 0.75 in the z-table.