A graph could represent a normal density function if it is symmetric about its​ mean, it has a single peak at the​ mean, the highest point occurs at the​ mean, and if it​ approaches, but does not ​ reach, the horizontal axis as x increases without bound and decreases without bound.

What does a normal density graph look like?

The normal curves are a family of symmetric, single-peaked bell-shaped density curves. A specific normal curve is completely described by giving its mean and its standard deviation. The mean and the median equal each other. The standard deviation fixes the spread of the curve.

Is a density curve normal?

A density curve is an idealized representation of a distribution in which the area under the curve is defined to be 1. Density curves need not be normal, but the normal density curve will be the most useful to us.