## Normal Distributions and the Empirical Rule

Maple Learn

How much did you weigh when you were born? How tall are you? What is your current blood pressure? It is well documented that in the general population, these variables – birth weight, height, and blood pressure – are normally or approximately normally distributed. This is the case for many variables in the natural and social sciences, which makes the normal distribution a key distribution used in research and experiments.

The Maple Learn Examples Gallery now includes a series of documents about normal distributions and related topics in the Continuous Probability Distributions subcollection.

The Normal Distribution: Overview will introduce you to the probability density function, cumulative distribution function, and the parameters of the distribution. This document also provides an opportunity for you to alter the parameters of a normal distribution and observe the resulting graphs. Try out a few real life examples to see the graphs of their distributions! For example, according to Statology, diastolic blood pressure for men is normally distributed with a mean of 80 mmHg and a standard deviation of 20 mmHg.

Next, the Normal Distribution: Empirical Rule document introduces the empirical rule, also referred to as the 68-95-99.7 rule, which describes approximately what percentage of normally distributed data lies within one, two, and three standard deviations of the distribution’s mean.

The empirical rule is frequently used to assess whether a set of data might fit a normal distribution, so Maple Learn also provides a Model Checking Exploration to help you familiarize yourself with applications of this rule.

In this exploration, you will work through a series of questions about various statistics from the data – the mean, standard deviation, and specific intervals – before you are asked to decide if the data could have come from a normal distribution. Throughout this investigation, you will use the intuition built from exploring the Normal Distribution: Overview and Normal Distribution: Empirical Rule documents as you analyze different data sets.

Once you are confident in using the empirical rule and working with normal distributions, you can conduct your own model checking investigations in real life. Perhaps a set of quiz grades or the weights of apples available at a grocery store might follow a normal distribution – it’s up to you to find out!

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