If nothing is known about a distribution except that it belongs to a certain class, then the maximum entropy distribution for that class is often chosen as a default, according to the principle of maximum entropy. The motivation is twofold: first, maximizing entropy minimizes the amount of prior information built into the distribution; second, many physical systems tend to move towards maximal entropy configurations over time.

The normal distribution N(μ,σ2) has maximum entropy among all real-valued distributions with specified mean μ and standard deviation σ. Therefore, if all you know about a distribution is its mean and standard deviation, it is often reasonable to assume that the distribution is normal.