Distributions that are "Mound-Shaped" and Symmetric

We had a preview of Normal Distributions when we looked at the "empirical rule" for distributions that are "mound-shaped and symmetric."

In the first half of 2020, the news was full of stories about "flattening the curve" of the COVID-19 pandemic. That "curve" was often pictured as a normal distribution. In this assignment Covid-19 and Flattening the Curve you will identify key features of normal distributions and determine how closely the actual data fit a normal-distribution model.

Features of a Normal Distribution

Normal distributions are the foundation of some very important methods of statistical inference. They can be described with an equation that depends on two population parameters (population mean and population standard deviation, but in this class you will never have to use that equation. Instead, you will need to use the key features of normal distributions. These are described here.

http://onlinestatbook.com/2/normal_distribution/intro.html

Additional features of a normal distribution include:

Almost all the area under the curve is within three standard deviations of the mean.
Changing the mean results in a horizontal shift in the graph.
Changing the standard deviation will change the steepness of the graph.
The graph has "inflection points" at +/- 1 standard deviations from the mean. That is, the shape of the graph changes from "up-cupped" to "down-cupped" or vice versa.

The Standard Normal Distribution

The Standard Normal Distribution (or z-distribution) is an important special case of a normal distribution that has a mean of 0 and standard deviation = 1

See https://www.flickr.com/photos/mitopencourseware/4479180432

Graph of standard normal distribution

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