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# Normal Distribution

As an example, we’ll start with the normal distribution. As you may remember from statistics classes, the probability density function for the normal distribution is:

To find the probability density at a given value, use the `dnorm` function:

`dnorm(x, mean = 0, sd = 1, log = FALSE)`

The arguments to this function are fairly intuitive: `x` specifies the value at which to evaluate the density, `mean` specifies the mean of the distribution, `sd` specifies the standard deviation, and `log` specifies whether to return the raw density (`log=FALSE`) or the logarithm of the density (`log=TRUE`). As an example, you can plot the normal distribution with the following command:

`> plot(dnorm, -3, 3, main = "Normal Distribution")`

The plot is shown in Figure 17-1.

The distribution function for the normal distribution is `pnorm`:

`pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)`

You can use the distribution function to tell you the probability that a randomly selected value from the distribution is less than or equal to q. Specifically, it returns p = Pr(xq). The value q is specified by the argument `q`, the mean by `mean`, and the standard deviation by `sd`. If you would like the raw value p, then specify `log.p=FALSE`; if you would like log(p), then specify `log.p=TRUE ...`