First, to understand the reason to use a normal distribuition, let's analyse some of it's properties.
The normal distribution is given by the following formula:
The normal distribuition is centered at the mean(given by 'mu' in the equation above) and its growth is controlled by its standard deviation(given by the 'sigma').
It is shaped like a bell(centered, with a gaussian decay, symetric). The data given by the question, have all of those properties. Is centered at the middle with a exponential decay in both 'directions'. Since the data agrees with the gaussian distribution properties, it makes sense to model this distribuition as a normal distribuition.