Q. What are the advantages of the normal distribution?
The first advantage of the normal distribution is that it is symmetric and bell-shaped. This shape is useful because it can be used to describe many populations, from classroom grades to heights and weights. The normal distribution (and related distributions) are also the easiest to use of the bell-shaped distributions. The standard normal density curve (with mean = 0 and standard deviation = 1) is pictured below.
The other main advantage of the normal distribution is the Central Limit Theorem. This theorem states that when the sample size is very large, the sample mean will generally follow a normal distribution even if the original population is not normally distributed. This means that we can often use inferential statistical methods that assume normality, even if the data in our sample doesn’t follow a normal distribution.
R Code for Graph:
x <- rnorm(10000000)
ggplot(data.frame(x=x)) + geom_density(aes(x=x)) + scale_x_continuous(breaks = c(-3,-2,-1,0,1,2,3), limits = c(-4,4)) + theme_bw()