Is global life expectancy normally distributed?
Let's see!

I took the most recent WHO data from here and did a quick an dirty analysis in R. Here is the histogram as well as a normal distribution with the same mean and standard deviation as the actual data:



Does not look very normally distributed. In fact, the shapiro test confirms this impression:

Shapiro-Wilk normality test

data:  df$life_expectancy
W = 0.94141, p-value = 4.338e-07




Edit

Commenters requested to weigh the life expectancy by population size.Well...the result is pretty ugly:



Apparently, the large populations of China and India produce disproportionally high bars. However, keep in mind that we are using averaged values which means that all the variation within countries is not represented by the histogram. We would actually have to have data on individual ages of death for a random sample of the world population to finally settle the question. :/