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.

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.

Exercise

Shape of normal distribution

Instructions 1/3

Question

Possible answers