You can use the following methods to work with the normal CDF (cumulative distribution function) in R:

**Method 1: Calculate Normal CDF Probabilities**

#calculate probability that random value is less than 1.96 in normal CDF pnorm(1.96) #calculate probability that random value is greater than 1.96 in normal CDF pnorm(1.96, lower.tail=FALSE)

**Method 2: Plot the Normal CDF**

#define sequence of x-values x <- seq(-4, 4, .01) #calculate normal CDF probabilities prob <- pnorm(x) #plot normal CDF plot(x, prob, type="l")

The following examples show how to use these methods in practice.

**Example 1: Calculate Normal CDF ****Probabilities **

The following code shows how to calculate the probability that a random variable takes on a value less than 1.96 in a standard normal distribution:

#calculate probability that random value is less than 1.96 in normal CDF pnorm(1.96) [1] 0.9750021

The probability that a random variables takes on a value less than 1.96 in a standard normal distrbution is **0.975**.

We can also find the probability that a random variable takes on a value greater than 1.96 by using the **lower.tail** argument:

#calculate probability that random value is greater than 1.96 in normal CDF pnorm(1.96, lower.tail=FALSE) [1] 0.0249979

And we can use the following syntax to find the probability that a random variable takes on a value between two values in a standard normal distribution:

#calculate probability that random value takes on value between -1.96 and 1.96 pnorm(1.96) - pnorm(-1.96) [1] 0.9500042

The probability that a random variable takes on a value between -1.96 and 1.96 in a standard normal distribution is **0.95**.

**Example 2: Plot the Normal CDF**

The following code shows how to plot a normal CDF:

#define sequence of x-values x <- seq(-4, 4, .01) #calculate normal CDF probabilities prob <- pnorm(x) #plot normal CDF plot(x, prob, type="l")

The x-axis shows the values of a random variable that follows a standard normal distribution and the y-axis shows the probability that a random variable takes on a value less than the value shown on the x-axis.

For example, if we look at x = 1.96 then we’ll see that the cumulative probability that x is less than 1.96 is roughly **0.975:**

Note that you can modify the aesthetics of the normal CDF plot as well:

#define sequence of x-values x <- seq(-4, 4, .01) #calculate normal CDF probabilities prob <- pnorm(x) #plot normal CDF plot(x, prob, type='l', col='blue', lwd=2, main='Normal CDF', ylab='Cumulative Prob')

**Additional Resources**

The following tutorials explain how to perform other common operations in R:

How to Plot a Normal Distribution in R

How to Calculate Z-Scores in R

A Guide to dnorm, pnorm, qnorm, and rnorm in R