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# Chapter 4: Probability Distributions

Difficulty Level: Basic Created by: CK-12

## Introduction

For a standard normal distribution, the data presented is continuous. In addition, the data is centered at the mean and is symmetrically distributed on either side of that mean. This means that the resulting data forms a shape similar to a bell and is, therefore, called a bell curve. Binomial experiments are discrete probability experiments that involve a fixed number of independent trials, where there are only 2 outcomes. As a rule of thumb, these trials result in successes and failures, and the probability of success for one trial is the same as for the next trial (i.e., independent events). As the sample size increases for a binomial distribution, the resulting histogram approaches the appearance of a normal distribution curve. With this increase in sample size, the accuracy of the distribution also increases. An exponential distribution is a distribution of continuous data, and the general equation is in the form \begin{align*}y = ab^x\end{align*}. The closer the correlation coefficient is to 1, the more likely the equation for the exponential distribution is accurate.

Chapter Outline

## Summary

This chapter details three key types of probability distributions: normal, binomial, and exponential. A normal distribution is a symmetric bell shape with the highest frequency in the center of a continuous distribution. A binomial distribution, covered last chapter, is like that with discrete values (success/failure). An exponential distribution is continuously growing or shrinking, and fits the general form \begin{align*}y= ab^x\end{align*}. The coefficient of determination \begin{align*}(r^2)\end{align*} is given by a calculator comparing points on the plot with the curve, and is a standard quantitative measure of best fit.

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