Normal Distributions and Probabilities in R

The R function pnorm() will be very helpful to use for calculating probabilities. In order to use it we need to tell the function a few specific things we are using:

• The value we are checking a probability for
• The mean of the normal distribution (default is zero)
• The standard deviation of the normal distribution (default is 1)
• Whether to give the probability less than or more than (by default R returns ‘less than’ probabilities, use “lower.tail=F” to get ’greater than probabilities)

Here is an example of using the pnorm() function to calculate the probability P(X < 7) for a normal distribution with a mean of 10 and std. dev. of 2. Note R by default finds “<” probabilities.

pnorm(7, mean = 10, sd = 2)

## [1] 0.0668072

Here is an example of using the pnorm() function to calculate the probability P(X > 25) for a normal distribution with mean 30 and std. dev. 10.

pnorm(25, mean=30, sd=10, lower.tail = FALSE)

## [1] 0.6914625

# Nice

When using a standard normal distribution, we do not need to specify mean and std. dev. in the pnorm function.

pnorm(-2)

## [1] 0.02275013

pnorm(2, lower.tail=F)

## [1] 0.02275013