# Calculating the magnitude of random numbers from normal distribution

Statement: Given an array of 80 random numbers, normally distributed between 0 and 1, we can expect that the numbers are all of similar magnitude, on the order of $80^{-1/2} \approx 0.1$.

Question: Where does the statement about "similar magnitude, on the order of $80^{-1/2} \approx 0.1$" come from?

Background: Statement is a paraphrase in "Numerical Linear Algebra" by Trefethen and Bau on Lecture 9 on MATLAB, page 65. I haven't studied much into random variable and probabilities and this is the first time the book is using any random variables.

My work so far:

So I shamelessly looked into "normal distribution calculator" (http://onlinestatbook.com/2/calculators/normal_dist.html) with the following input:

Mean: 0.5

Standard Deviation 0.1

Between 0 and 1

The graph showed the entire distribution between 0 and 1 being covered by one standard deviation. Is this what "similar magnitude" the book is referring to? What's the point of using the number 80 then?

• That doesn't quite explain the role of $80$, the size of array, which is used to estimate the order of magnitude of a random variable between $0$ and $1$. Even strictly applying the quoted explanation, it doesn't work at all for $0$ and $1$.