How is a Bimodal distribution platykurtic? I am trying to understand how the distribution on the right is platykurtic? I learned that platykurtic indicates lighter and thinner tails and from what it looks like, the bimodal distribution, with a superimposed normal curve, seems to have a lot more values in the tails?
Is it light-tailed by the fact that each mode is skewed? Thank you.


Graphical comment per @whuber's Comment.
Here is a histogram of a sample of a million observations from a
beta distribution with shape parameters $\alpha=\beta = 0.5.$ The Wikipedia link has formulas for the mean, variance, skewness, and kurtosis of beta distributions (for given $\alpha,\beta)$. The superimposed normal density curve matches the mean and SD of
the sample.

R code for figure:
set.seed(2021)
y = rbeta(10^6, .5, .5)
mean(y); sd(y)
[1] 0.500134
[1] 0.3535411
hdr = "BETA(.5, .5) Sample with Normal PDF"
hist(y, prob=T, br=30, xlim=c(-.5,1.5), col="skyblue2", main=hdr)
 curve(dnorm(x, mean(y), sd(y)), add=T, col="orange", lwd=2)
 abline(h=0, col="green2")

