Normal distributions as models for data
The family of normal distributions consists of symmetric bell-shaped distributions that are defined by two parameters, µ and σ. The mean and standard deviation of a normal distribution are equal to µ and σ, respectively.
Data sets are sometimes assumed to be random samples from populations that have normal distributions.
Teabag weight
Data with skew distributions can often be transformed into a fairly symmetrical form. A normal distribution may be a reasonable model for the transformed data.
Summary statistics
A more important reason for the importance of the normal distribution in statistics is that many summary statistics have normal distributions (at least approximately).