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# The Normal Distribution

In This Chapter

• Understanding the normal and standard normal distributions
• Going from start to finish when finding normal probabilities
• Working backward to find percentiles

In your statistical travels you'll come across two major types of random variables: discrete and continuous. Discrete random variables basically count things (number of heads on 10 coin flips, number of female Democrats in a sample, and so on). The most well-known discrete random variable is the binomial. (See Chapter 8 for more on discrete random variables and binomials). A continuous random variable is typically based on measurements; it either takes on an uncountably infinite number of values (values within an interval on the real line), or it has so many possible values that it may as well be deemed continuous (for example, time to complete a task, exam scores, and so on).

In this chapter, you understand and calculate probabilities for the most famous continuous random variable of all time — the normal distribution. You also find percentiles for the normal distribution, where you are given a probability as a percent and you have to find the value of X that's associated with it. And you can think how funny it would be to see a statistician wearing a T-shirt that said “I'd rather be normal.”

## Exploring the Basics of the Normal Distribution

A continuous random variable X has a normal distribution if its values fall into a smooth (continuous) curve with a bell-shaped pattern. ...

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