The **pnorm() function** calculates the c. d. f. where X is normal. Optional arguments described on the online documentation specify the parameters of the particular normal distribution.

**pnorm in R**

The **pnorm in R** is a **built-in function** **that returns the value of the cumulative density function** (cdf) of the normal distribution given a certain random variable **q**, and a population mean **μ**, and the population standard deviation **σ**.

**Syntax**

`pnorm(q, mean, sd, lower.tail = TRUE, log.p = FALSE) `

**Parameters**

**q:** It is a vector of quantiles.

**mean:** It is a vector of means.

**sd:** It is a vector of standard deviations.

**lower.tail:** It is logical; if TRUE (default), probabilities are otherwise.

**log, log.p:** It is a logical argument.

If **mean** or **sd** are not specified, they assume the default values of 0 and 1, respectively.

**Example**

Find the percentage of males taller than 78 inches in a population with mean = 74 and sd = 2.

`pnorm(78, mean = 74, sd = 2, lower.tail = FALSE)`

**Output**

`[1] 0.02275013`

Find the percentage of otters that weight less than 33 lbs in a population with mean = 40 and sd = 8. Let’s see the following code example.

`pnorm(33, mean=40, sd = 8)`

**Output**

`[1] 0.190787`

The pnorm() function returns the integral from **−∞** to q of the pdf of the normal distribution where q is a Z-score. Try to guess the value of pnorm(0).

`pnorm(0)`

**Output**

`[1] 0.5`

The pnorm() function also takes the argument **lower.tail**. If the **lower.tail** is set equal to **FALSE,** then pnorm returns the integral from q to ∞ the pdf of the normal distribution.

Note that pnorm(q) is the same as 1-pnorm(q, lower.tail = **FALSE**).

`pnorm(2)`

**Output**

`[1] 0.9772499`

That is it for the pnorm() function in R.

**See also**

Krunal Lathiya is an Information Technology Engineer by education and web developer by profession. He has worked with many back-end platforms, including Node.js, PHP, and Python. In addition, Krunal has excellent knowledge of Data Science and Machine Learning, and he is an expert in R Language. Krunal has written many programming blogs, which showcases his vast expertise in this field.