How to use the pnorm() function in R to verify the empirical rule?

Question

I have no clue how to use pnorm() to do this. Empiral rule: 68% of observations are within 1 standard deviation of the mean. 95% of observations are within 2 standard deviations of the mean. 99.7% of observations are within 3 standard deviations of the mean.

Answer 1

pnorm is a function which essentially gives you the value of the CDF of the normal distribution at a given point. The default is for a standard normal distribution. Thus,

pnorm(0)
#> [1] 0.5

is essentially telling you that 50% of the mass of the standard normal distribution lies below 0. To get the mass between two numbers, say the mass between -1.5 and 2 one would do

pnorm(2) - pnorm(-1.5)
#> [1] 0.9104427

As I'm guessing this is a homework question, that should be enough to get you on your way to verifying the empirical rule.