The **rnorm()** function generates a random number using a normal(bell curve) distribution. Thus, the **rnorm()** function simulates random variates having a specified normal distribution.

**What is Normal Distribution in R**

The normal distribution is the collection of random data from independent sources is distributed normally. We get the bell shape curve by plotting a graph with the variable’s value on the horizontal axis and the values’ count on the vertical axis. The center of the curve represents the mean of the dataset.

**Functions in R for Probability Distributions**

R distribution handles four functions to generate random numbers. First, there is a root name. The root name for the normal distribution is the **norm**. This root is prefixed by one of the following letters.

- The
**p**is for “**probability**“, and it is a cumulative distribution function. For example,**pnorm()**function.

- The
**q**is for “**quantile**“, and it is an inverse. For example,**qnorm()**function.

- The
**d**is for “**density**“, and it is a density function. For example,**dnorm()**function.

- The
**r**is for “**random**“, and it is a random variable having the specified distribution. For example,**rnorm()**function.

We will talk about **rnorm()** in this tutorial. As with **pnorm()**, **qnorm()**, and **dnorm()**, the optional arguments define the mean and standard deviation of the distribution.

**rnorm in R**

The **rnorm()** is a built-in R function that generates a vector of normally distributed random numbers. The rnorm() method takes a sample size as input and generates that many random numbers.

It generates the **Normal** **Distributions** On Special Spaces. The **rnorm()** function helps to generate random numbers whose distribution is normal.

**Syntax**

`rnorm(n, mean, sd)`

**Parameters**

**n:** It is the number of observations(sample size).

**mean:** It is the mean value of the sample data. Its default value is zero.

**sd:** It is the standard deviation. Its default value is 1.

**Example**

```
data <- rnorm(10)
data
```

**Output**

```
[1] -0.359721535 1.516744916 -0.380787719 0.345410241 0.321703671 -0.436644645 -0.267328311
[8] -1.640269174 -0.190012636 -0.004461941
```

**Create a histogram based on rnorm()**

To create a histogram in R, use the hist() function. A histogram depicts the frequencies of values of a variable bucketed into ranges. The histogram is similar to the bar chart, but it groups the values into continuous ranges.

To create a normal distribution in R, use the rnorm() function. Let’s generate 30 random numbers using the rnorm() function and create a histogram based on that distribution.

```
data <- rnorm(30)
hist(data, main="Normal distribution")
```

**Output**

And we get the bar chart type of histogram based on the random data.

**Generate three different vectors of random numbers in R**

Let’s generate three different vectors of random numbers in R using the rnorm() function.

Let’s generate histograms based on these random numbers.

```
k10 <- rnorm(10, mean = 50, sd = 8)
k100 <- rnorm(100, mean = 50, sd = 8)
k1000 <- rnorm(10000, mean = 50, sd = 8)
oldpar <- par()
par(mfrow=c(1,3))
# The breaks argument specifies how many bars are in the histogram
hist(k10, breaks = 5)
hist(k100, breaks = 20)
hist(k1000, breaks = 80)
```

**Output**

You can see that we have created three histograms using three different normal distributions.

**Conclusion**

To generate a vector of normally distributed random numbers in R, use the rnorm() function. The first argument n is the number of numbers you want to generate, followed by the standard **mean** and **sd** arguments.

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