Solved – What does the y-axis of a normal distribution represent?

central limit theoremdistributionsnormal distribution

In a normal distribution ,as far as I know distribution represents frequency of sth.But then how come normal distribution y-axis becomes

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If distribution y-axis doesnt represent frequency, the what is central limit theorem.The central limit theorem y-axis represents the frequency of mean samples.Shouldnt it represent the above formula to satisfy a normal distribution

Best Answer

As you can see from the definition of the normal density, it is not dimension-less, but its measurment unit (dimension in the physical meaning) is the same as that of $1/\sigma$ which in turn is the same dimension as that of $1/x$. Integrating over $f(x)$ yields a dimensionless quantity: the probability of the region of integration.

The y-axis is thus "probabilty per measurement unit of x". This holds for every probability density, not only the normal density.