Normal Distribution

A normal distribution is a unimodal and symmetric, bell shaped curve.

We write this as:

$$N(\mu, \sigma)$$

𝜇: mean

𝜎: Standard Deviation

# A Graph of a normal distribution of mean 3 and standard deviation 5
using Plots
using StatPlots
using Distributions
gr()
plot(Normal(3,5), title="Normal Distribution N(3,5)", lw=3,)
┌ Info: Precompiling StatPlots [60ddc479-9b66-56df-82fc-76a74619b69c]
└ @ Base loading.jl:1186

svg

Lots of things have nearly normal distributions. SAT scores are distributed nearly normally with mean 1500 and standard deviation of 300.

# A graph of the SAT distribution
𝜇=1500
𝜎=300
plot(Normal(𝜇,𝜎), title="Normal Distribution N($(𝜇),$(𝜎))", lw=3, label=["SAT Distribution"])
vline!([1200,1800], label="1 Standard Deviation")
vline!([900, 2100], label="2 Standard Deviations")
vline!([600, 2400], label="3 Standard Deviations")

svg