Here is a path as to how to visually determine whether bell-shaped curves are normal.
Start by drawing equal probability mass cut points on the graph. This produces quantile (cut point) estimates. Per a source, to quote:
In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile than the number of groups created.
Next, examine the cut-points and visually (or more rigorously) construct a QQ Plot. Per an educational source:
One way to assess how well a particular theoretical model describes a data distribution is to plot data quantiles against theoretical quantiles...For a large sample from the theoretical distribution the plot should be a straight line through the origin with slope 1...
where the theoretical distribution here is taken to be the Normal distribution.
To obtain a probability that the slope estimate per a Least-Squares fit is indeed here equal to 1, more work can be performed as detailed in this source: Non-Zero Null Tests for Simple Linear Regression.
Optionally, I suggest you actually simulate a Normal and other distributions based on the sample size used to construct the graph, and test for accuracy over repeated runs the suggested methodology.
I hope this answer is of assistance.