# How to Use pnorm in R (Examples)

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).
• log.p: The default value is FALSE. If log.p=TRUE, p generated by the function is a log-value.

## 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.