Question

Verify the empirical rule by using Table A, software, or a calculator to show that for a normal distribution, the probability (rounded to two decimal places) within

a. 1 standard deviation of the mean equals 0.68.

b. 2 standard deviations of the mean equals 0.95.

c. 3 standard deviations of the mean is very close to 1.00.

I need the copy and paste your R command and output

Answer 1

## the simplest code is written using the pnorm() function in R ,

pnorm(1) - pnorm(-1)

## within 2 standard deviation
pnorm(2) - pnorm(-2)

## within 3 standard deviations
pnorm(3) - pnorm(-3)

The results are

> pnorm(1) - pnorm(-1)
[1] 0.6826895
> pnorm(2) - pnorm(-2)
[1] 0.9544997
> ## within 3 standard deviations
> pnorm(3) - pnorm(-3)
[1] 0.9973002

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