Final answer:
The normal distribution is symmetrical, commonly used across multiple disciplines, and is defined by its mean and standard deviation. The standard deviation affects the curve's shape, while the mean affects its location.
Step-by-step explanation:
The normal distribution is a fundamental concept in probability and statistics, characterized by a symmetric, bell-shaped curve where the mean, median, and mode all coincide at the center. The properties of a normal distribution include symmetry around the mean, prevalence across various disciplines like psychology, business, and science, and it's entirely defined by two parameters - the mean (µ) and the standard deviation (σ). These parameters determine the location and the spread of the distribution, respectively. Outliers do not affect the shape of a normal distribution because it is based on the mean and standard deviation, which encapsulate all data points within the distribution.
The importance of the normal distribution lies in its commonality and its use in statistics. It is used to approach problems involving natural and social phenomena. Due to its characteristics, the Empirical Rule can be applied, stating that approximately 68% of data lies within one standard deviation, about 95% within two standard deviations, and over 99% within three standard deviations from the mean.
The normal distribution's shape can be affected by changes in the standard deviation and mean. A larger standard deviation results in a flatter and wider distribution, while a smaller standard deviation produces a steeper and narrower curve. Altering the mean will shift the entire distribution left or right without changing its shape.