pnorm() function calculates the probability of a normally distributed number q, with a specified mean and standard deviation.
Syntax
pnorm(x, mean = , sd = , lower.tail= )Arguments
- q = numeric value to test for probability
- mean = mean of the distribution
- sd = standard deviation of the distribution
- lower.tail = TRUE or FALSE
The mean, sd, and lower.tail arguments are optional. If you do not pass a value to them, they will take the default values as mean = 0, sd = 1 and lower.tail = TRUE.
Given the value of q, pnorm returns the probability of that value or less. For example, let’s say the snow height value is given as q. Passing the pnorm() function will return the probability of the snow height q or less, i.e., the left side of the distribution. However, to calculate the right side of the distribution or the probability of snow height q or greater, you have to change lower.tail argument to TRUE.
Examples
Suppose snow heights in your area are normally distributed with a mean of 56 inches and a standard deviation of 8.
Example 1: What is the probability that the snow height will be less than or equal to 45 inches?
pnorm(45, mean = 56, sd = 8)Output
[1] 0.08456572Example 2: What is the probability that the snow height will be greater than or equal to 45 inches?
pnorm(45, mean = 56, sd = 8, lower.tail = FALSE)Output
[1] 0.9154343In Example 2, we assigned lower.tail argument as FALSE because we wanted to calculate the right side of the distribution.