Exercise

# Shape of normal distribution

All **normal distributions** are symmetric and have a bell-shaped density curve with a single peak.

The normal distribution takes two parameters: the **mean** (\(\mu\)) and the **variance** (\(\sigma^2\)).
The notation of the normal distribution is \(N(\mu, \sigma^2)\). The mean indicates where the peak of the density curve occurs, and the variance indicates the spread of the bell curve.

The **standard deviation** (\(\sigma\)) is the square root of **variance** (\(\sigma^2\)). The `rnorm()`

function takes the standard deviation (`sd`

) as an argument.

We will review *descriptive statistics* in the next chapter.

In this exercise, you will generate samples from three different normal distributions and visualize their distributions.
The libraries `tidyr`

and `ggplot2`

have been preloaded for this exercise.

Instructions 1/3

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#### Question

How do the mean and the standard deviation impact the density curve of the normal distribution?

##### Possible Answers

- A lower mean shifts the graph to the left. A lower standard deviation flattens the curve.
- A higher mean shifts the graph to the left. A higher standard deviation flattens the curve.
- A higher mean shifts the graph to the right. A higher standard deviation flattens the curve.