Effect of units on shape of normal distribution

Question

TL;DR: Is the shape of a bell curve / normal distribution idependent of the units chosen to represent a certain variable?

More detail: I was playing around with some data from this paper in excel:

	Transmission (R)	Temperature (C)	Humidity (%)
mean	1.831	6.017	78.456
stdev	0.522	6.549	9.898

When I plot a normal distribution for each of these variables, I see that the greater the stdev, the flatter the curve:

In this case, humidity has the greatest stdev, so it has the flattest curve. This follows what I have learned in my (limited) stats education, but intuitively it seems wrong to me. Sure, humidity has a greater stdev than temperature, but the units are completely different, so it seems like an unfair comparison. Furthermore, if I simply change the units of humidity from a percent to a decimal it now has the smallest stdev (mean=0.78456, stdev=0.09898). When I try this in excel this actually changes the shape of the curve, with humidity now being the steepest rather than the flattest. It seems wrong to me that changing the units should actually change the shape of the distribution.

Answer 1

Comment continued: Here are density curves of normal distributions with different standard deviations, plotted on the same scale. [Plot in R.]

hdr="Densities of NORM(0,1) [red], NORM(0,3) [green], and NORM(0,5)"
curve(dnorm(x), ylab="PDF", -15,15, col="red", n=10001, lwd=2, main=hdr)
 curve(dnorm(x,0,3), add=T, col="darkgreen", lwd=2)
 curve(dnorm(x,0,5), add=T, col="blue", lwd=2)
  abline(h=0, col="green2");  abline(v=0, col="green2")

Answer 2

Recall that the probability density function tells us about "probability per foot" and that it has the property that it integrates to one. What follows, the $y$-axis units, the probability densities will depend on the units on $x$-axis. Imagine a simplified example, the uniform density, if you plot it, it's a rectangle, if you increase the units on $x$-axis, to preserve the area equal to one, the $y$-axis units would need to decrease. The same happens with the Gaussian curve, making it wider will make it flatter. Nothing else changes about the Gaussian except being wider and flatter vs thinner and spikier.

As for the attached plots, what was already noticed in the comments, they seem to be wrong, because they do not show the property described above. Moreover, as a general rule, it is not a good practice to use a shared axis to display different units, if this is what the authors are doing.