This tutorial shows the definition of pnorm() in R and how to use it with examples. pnorm() is used to return probability (** p**) for the given quantile (

**).**

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

**q:**the quantile (value on the x-axis)**mean:**The mean of the sample data. The default value is 0.**sd:**The standard deviation. The default value is 1.**lower.tail:**By default, lower.tail = TRUE. If lower.tail = TRUE, CDF is calculated from left (lower tail) to right (higher tail).- l
**og.p**: The default value is FALSE. If log.p=TRUE,**p**generated by the function is a log-value.

## Examples of how to use pnorm in R

## Example 1

The following is the R code example of pnorm(). In particular, it returns the probability value for the CDF in the range of (-**∞**, 0) for the standard normal distribution (i.e., mean = 0 and sd =1).

> pnorm(0, 0, 1) [1] 0.5

The following is the plot for pnorm(0, 0, 1). The area of the blue shade is 0.5.

## Example 2

The following returns the CDF value for (-**∞**, 2). The value is 0.977, which is a probability value.

> pnorm(2, 0, 1) [1] 0.9772499

The following is the plot for pnorm(2, 0, 1). The area of red shade is 0.977.

## Example 3: **lower.tail = **TRUE in pnorm()

By default, `lower.tail = TRUE`

. It means that probability CDF is calculated from left (lower tail) to right (higher tail). Thus, without and with `lower.tail = TRUE`

will generate the same result.

> pnorm(2, 0, 1) [1] 0.9772499 > pnorm(2, 0, 1,lower.tail = TRUE) [1] 0.9772499

## Example 4: **lower.tail = **FALSE in pnorm()

If `lower.tail = FALSE`

, probability CDF is calculated from right (higher tail) to left (lower tail). Thus, `lower.tail = FALSE`

and `lower.tail = TRUE`

will generate opposite results.

> pnorm(2, 0, 1,lower.tail = TRUE) [1] 0.9772499 > pnorm(2, 0, 1,lower.tail = FALSE) [1] 0.02275013

## Example 5: **log.p = FALSE** in pnorm()

If `log.p = FALSE`

, it will return log(p). The following is the R code example.

> pnorm(2, 0, 1,log.p = FALSE) [1] 0.9772499 > pnorm(2, 0, 1,log.p = TRUE) [1] -0.02301291

Note that, log(0.9772499) = -0.02301288, which is very close to -0.02301291.